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Prokopjeva, Evgenija, Evgeny Tankov, Tatyana Shibaeva, and Elena Perekhozheva. "Behavioral models in insurance risk management." Investment Management and Financial Innovations 18, no. 4 (October 21, 2021): 80–94. http://dx.doi.org/10.21511/imfi.18(4).2021.08.
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Behavioral characteristics attributed to consumers of insurance services are a relevant factor for analyzing the current situation in the insurance market and developing effective strategies for insurers’ actions. In turn, considering these characteristics allows the insurer to be more successful in the highly competitive field, achieving mutual satisfaction in interacting with the customer. This study is aimed to develop cognitive models of the situation (frame) “Insurance”, taking into account the specifics of the Russian insurance market and systemic factors affecting participants’ behavior in the market. In this regard, the study involves systemizing risks at various levels of the economic system, generalizing factors for the motivation of insurance consumers, developing descriptive and economic-mathematical models for the behavior of economic entities in risky situations.The results obtained represent a behavioral model of interactions among insurance market entities, which determines opportunities for efficient and mutually beneficial coordination of their activities. The developed model includes the following elements: structured individual and institutional frames “Insurance”; a professional index of interest in insurance presented in the form of a mathematical model; methodology for governing the relationships among insurance participants in the digital environment.The recommendations enable predictions of the situation in the insurance market and allow most accurately defining the consumer needs in the conditions of market changes.
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Drissi, Ramzi. "Mathematical Risk Modeling: an Application in Three Cases of Insurance Contracts." International Journal of Advances in Management and Economics 8, no. 6 (October 30, 2019): 01–10. http://dx.doi.org/10.31270/ijame/v08/i06/2019/1.
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Risk is often defined as the degree of uncertainty regarding the future. This general definition of risk can be extended to define different types of risks according to the source of the underlying uncertainty. In this context, the objective of this paper is to mathematically model risks in insurance. The choice of methods and techniques that allow the construction of the model significantly influence the responses obtained. We approach these different issues by modeling risks in three base cases: basic insurance of goods, life insurance, and financial risk insurance. Our findings show that risk modeling allowed us to better measure certain events, but did not allow us to predict them accurately due to a lack of information. Therefore, good modeling of the risk determinants makes it possible to modify the probability associated with the occurrence of a risk. While it cannot predict exactly when a risk will occur, it can help make decisions that will reduce its effects. Keywords: Basic insurance, Life insurance, Mathematical models, Financial risk, Biometric function.
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Zhuk, Tetyana. "Mathematical Models of Reinsurance." Mohyla Mathematical Journal 3 (January 29, 2021): 31–37. http://dx.doi.org/10.18523/2617-70803202031-37.
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Insurance provides financial security and protection of the independence of the insured person. Its principles are quite simple: insurance protects investments, life and property. You regularly pay a certain amount of money in exchange for a guarantee that in case of unforeseen circumstances (accident, illness, death, property damage) the insurance company will protect you in the form of financial compensation.Reinsurance, in turn, has a significant impact on ensuring the financial stability of the insurer. Because for each type of insurance there is a possibility of large and very large risks that one insurance company can not fully assume. In the case of a portfolio with very high risks, the company may limit their acceptance, or give part of the reinsurance. The choice of path depends entirely on the company’s policy and type of insurance.This paper considers the main types of reinsurance and their mathematical models. An analysis of the probability of bankruptcy and the optimal use of a particular type of reinsurance are provided.There are also some examples and main results of research on this topic. After all, today the insurance industry is actively gaining popularity both in Ukraine and around the world. Accordingly, with a lot of competition, every insurer wants to get the maximum profit with minimal e↵ort.
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Chen, Liansheng, and Jinhua Tao. "Mixed Insurance Risk Models." Missouri Journal of Mathematical Sciences 8, no. 1 (February 1996): 3–10. http://dx.doi.org/10.35834/1996/0801003.
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Korstanje, Maximiliano Emanuel, and Babu P. George. "What does insurance purchase behaviour say about risks?" International Journal of Disaster Resilience in the Built Environment 6, no. 3 (September 14, 2015): 289–99. http://dx.doi.org/10.1108/ijdrbe-09-2012-0030.
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Purpose – This paper aims to explore the world of insurances as rites of adaptancy and resiliency before risk and disasters. The research on risks, both perceived and real, has become a frequent theme of academic research in the recent past. Design/methodology/approach – The information given by the superintendencia de Seguros de Buenos Aires involves 100 per cent of the insurances companies of Argentina. The reading of insurance demands corresponds with a new method in the studies of risks. Findings – Using advanced probability theory and quantitative techniques, risk management researchers have been able to construct sophisticated mathematical-statistical models of risk. Research limitations/implications – However, the relation between anticipated risks and insurance purchase behaviour has not received sufficient attention. In the present study, starting from the premise that societies may be studied by examining their fears, the authors posit that these fears are represented in the insurance premiums people buy for being protected. Originality/value – Insurance purchase behaviour at any particular point in time is a measure of what a society considers to be risky at that time and is a key source of information for tourism managers.
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Lefèvre, Claude, and Philippe Picard. "RISK MODELS IN INSURANCE AND EPIDEMICS: A BRIDGE THROUGH RANDOMIZED POLYNOMIALS." Probability in the Engineering and Informational Sciences 29, no. 3 (March 23, 2015): 399–420. http://dx.doi.org/10.1017/s0269964815000066.
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The purpose of this work is to construct a bridge between two classical topics in applied probability: the finite-time ruin probability in insurance and the final outcome distribution in epidemics. The two risk problems are reformulated in terms of the joint right-tail and left-tail distributions of order statistics for a sample of uniforms. This allows us to show that the hidden algebraic structures are of polynomial type, namely Appell in insurance and Abel–Gontcharoff in epidemics. These polynomials are defined with random parameters, which makes their mathematical study interesting in itself.
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Shkolnyk, Inna, Eugenia Bondarenko, and Valery Balev. "Estimation of the capacity of the Ukrainian stock market’s risk insurance sector." Insurance Markets and Companies 8, no. 1 (November 24, 2017): 34–47. http://dx.doi.org/10.21511/ins.08(1).2017.04.
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The purpose of the article is to determine the degree of financial interaction between the stock and insurance market, or, in other words, to determine the potential capacity of the stock market’s risk insurance sector for the Ukrainian insurance market. The authors examine the insurance not of all possible risks on the stock market, but only the most potentially important for the development of the stock market at this stage of economic development: insurance of professional risks of depositories and insurance of individual investments of individuals – participants of the stock market. In order to calculate the capacity of the stock market’s risk insurance sector in the context of the two above mentioned types, the authors apply the models that are widely used in the economic-mathematical analysis. For mathematical calculations we used 31 absolute indicators of the characteristics of the state of the stock and insurance markets, as well as some macroeconomic indicators. When forming an array of input data for mathematical calculations we used annual values of absolute indicators for the period 2005–2015 were used. For the adequacy of the received calculations the normalization of the selected indicators was carried out. All indicators were divided into two groups: stimulators and de-stimulators. The normalization of stimulator indicators was carried out by the method of natural normalization, and of de-stimulator indicators – according to the Savage formula. The capacity of the segment of the new type of insurance was determined by the authors as the maximum possible amount of insurance premiums that insurers can get in the process of implementing a new insurance product based on the current state of development of the insurance market. The capacity of the sector of the new type of insurance was presented as a function of the main component (an indicator that directly characterizes the created segment) and the corrective component (a set of indicators characterizing the segments created indirectly). The weight coefficients of the corrective component were determined by using the Fischer’s formula. As a result of the calculations, the authors obtained the data on the prospects of simultaneous introduction for the stock and insurance markets of such types of insurance as a professional liability insurance of depositories and an insurance of individual investors on the stock market.
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Nkeki, C. I., and G. O. S. Ekhaguere. "Some actuarial mathematical models for insuring the susceptibles of a communicable disease." International Journal of Financial Engineering 07, no. 02 (May 18, 2020): 2050014. http://dx.doi.org/10.1142/s2424786320500140.
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Using epidemiological and actuarial analysis, this paper formulates some new actuarial mathematical models, called S-I-DR-S models, for insuring the susceptibles of a population exposed to a communicable disease. Epidemiologically, the population is structured into four demographic groups, namely: susceptibles [Formula: see text], infectives [Formula: see text], diseased [Formula: see text] and recovered [Formula: see text], with the latter automatically re-entering the group of susceptibles [Formula: see text]. The insurance policies are targeted at the members of the susceptible group who face the risk of infection and death due to the disease. Using actuarial techniques and principles, we determine some interesting features of the model, namely, (a) financial obligations of the parties, (b) present value of premiums, (c) quantum of claims by infected policy holders (PHs), (d) quantum of claims on behalf of deceased PHs, (e) cumulative insurance reserve for annuity and (f) lump sum plan. To check the risk of insolvency, premium adjustment for the PHs is also considered.
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Singh, Amrik, and K. R. Ramkumar. "Risk assessment for health insurance using equation modeling and machine learning." International Journal of Knowledge-based and Intelligent Engineering Systems 25, no. 2 (July 26, 2021): 201–25. http://dx.doi.org/10.3233/kes-210065.
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Due to the advancement of medical sensor technologies new vectors can be added to the health insurance packages. Such medical sensors can help the health as well as the insurance sector to construct mathematical risk equation models with parameters that can map the real-life risk conditions. In this paper parameter analysis in terms of medical relevancy as well in terms of correlation has been done. Considering it as ‘inverse problem’ the mathematical relationship has been found and are tested against the ground truth between the risk indicators. The pairwise correlation analysis gives a stable mathematical equation model can be used for health risk analysis. The equation gives coefficient values from which classification regarding health insurance risk can be derived and quantified. The Logistic Regression equation model gives the maximum accuracy (86.32%) among the Ridge Bayesian and Ordinary Least Square algorithms. Machine learning algorithm based risk analysis approach was formulated and the series of experiments show that K-Nearest Neighbor classifier has the highest accuracy of 93.21% to do risk classification.
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Khanlarzadeh, Sarvinaz. "Mathematical Modeling of the Risk Reinsurance Process." WSEAS TRANSACTIONS ON MATHEMATICS 21 (June 20, 2022): 447–60. http://dx.doi.org/10.37394/23206.2022.21.52.
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This paper presents a method for assessing financial risks and managing them to optimize the decision-making process. It is shown that the type of economic entity at risk and its activities in the financial market affect the specifics of financial risk management, which can be classified into three main groups: hedging, diversification, and insurance. The main instruments used for this purpose are also identified. Special attention is given to the dynamic properties of financial flows arising from the simulation of artificial financial instruments, as well as to their influence on the results of financial risk management when taking into account errors in estimating parameters of mathematical models. The purpose of our study is to create a mathematical model that can be used to assess the risk reinsurance process. We will create a mathematical model of the risk reinsurance process using the following steps: 1. Identify all of the relevant variables in our analysis. 2. Determine how these variables interact with each other and come to a conclusion about how they influence each other's values. 3. Find equations that represent these relationships between the variables and solve for their values with those equations. 4. Test these models against real data from known cases in order to ensure that they work as expected, then use them for future studies or applications requiring this type of modeling technique.
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Klepikova, O. А., and Z. M. Sokolovska. "The Information and Analytical Model of the Decision-Making Process for the Development of Health Insurance Programs." Business Inform 1, no. 516 (2021): 119–33. http://dx.doi.org/10.32983/2222-4459-2021-1-119-133.
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The article is aimed at studying and automating the stages of decision-making process for the development and implementation of health insurance products using the economic, mathematical, and simulation modeling. When analyzing the scientific works of scholars on the development of health insurance in Ukraine, the main stages of the decision-making process are allocated, the major of them are: the market need for an insurance product in the external environment; clear definition of the company’s tactical and strategic goals; examining the properties and characteristics of the insurance product; risk assessment and profitability of the insurance product. In the course of the study, the modeling of risk assessment, profitability of health insurance programs and analysis of the obtained results were carried out in detail. It is substantiated that a comprehensive analysis of the risk and profitability of health insurance programs will allow to form the necessary insurance reserves, to ensure the competitive position of an insurance company and to fulfill the targeted goals. If statistical information is available, any health insurance programs, including the COVID-19 insurance programs that require an assessment of pandemic risk, which requires special attention from both society and insurance, can be analyzed. It should be noted that modeling is a key element for assessing and managing pandemic risk. Prospects for further research in this direction are the expansion of the base of economic, mathematical and analytical models for assessing the risk of insurance portfolio and the inclusion in the simulation model of a wider range of factors of both the external and the internal environment.
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Xie, Shengkun. "Improving Explainability of Major Risk Factors in Artificial Neural Networks for Auto Insurance Rate Regulation." Risks 9, no. 7 (July 2, 2021): 126. http://dx.doi.org/10.3390/risks9070126.
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In insurance rate-making, the use of statistical machine learning techniques such as artificial neural networks (ANN) is an emerging approach, and many insurance companies have been using them for pricing. However, due to the complexity of model specification and its implementation, model explainability may be essential to meet insurance pricing transparency for rate regulation purposes. This requirement may imply the need for estimating or evaluating the variable importance when complicated models are used. Furthermore, from both rate-making and rate-regulation perspectives, it is critical to investigate the impact of major risk factors on the response variables, such as claim frequency or claim severity. In this work, we consider the modelling problems of how claim counts, claim amounts and average loss per claim are related to major risk factors. ANN models are applied to meet this goal, and variable importance is measured to improve the model’s explainability due to the models’ complex nature. The results obtained from different variable importance measurements are compared, and dominant risk factors are identified. The contribution of this work is in making advanced mathematical models possible for applications in auto insurance rate regulation. This study focuses on analyzing major risks only, but the proposed method can be applied to more general insurance pricing problems when additional risk factors are being considered. In addition, the proposed methodology is useful for other business applications where statistical machine learning techniques are used.
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Dashko, Vitaly Mikhailovich. "Modeling of fire risk management support in the residential sector during individual insurance." Technology of technosphere safety 97 (2022): 160–70. http://dx.doi.org/10.25257/tts.2022.3.97.160-170.
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Introduction. A significant factor influencing the reduction of the risk of death in case of fires in the residential sector is the presence of fire alarm systems (FAS) in residential premises. Ensuring FAS in the course of insurance is one of the effective ways to improve the level of fire safety in the residential sector. The relevance of the study lies in the development of a support model for fire risk management in the residential sector in the course of individual insurance of residential real estate in the Russian Federation. Goals and objectives. The purpose of the article is the development of calculation models for determining the economic effect for the insurer and the insured from the presence of FAS at the insurance object and the development of a support model for fire risk management in the residential sector based on the individual insurance system. This goal allows us to solve the problem of improving the level of fire safety in the residential sector on the territory of the Russian Federation. Methods. The basis of theoretical research was the methods of system analysis, mathematical statistics, socio-economic analysis and mathematical modeling. The basis of the study was domestic and foreign sources, statistical materials and the results of research work on the subject of the study. Results and discussion. Solutions have been found to support the management of fire risks in the residential sector in the course of individual insurance of residential real estate. And new scientifically substantiated results of the implementation of the tasks set are presented, the solution of which is essential for improving the level of fire safety in the Russian Federation. Conclusions. The results of solving a scientific problem to support the management of fire risks in the residential sector in the course of individual insurance in the territory of the Russian Federation are presented. The decision is based on economic motivation, both insurers and policyholders. Calculation models for determining the economic effect for the insurer and the insured from the presence of FAS at the insurance object are proposed and a model is developed to support the management of fire risks in the residential sector based on the individual insurance system, which allows achieving voluntary, economically motivated fulfillment of fire safety requirements. The socio-economic expediency of the developed model is shown. Keywords: fires, loss of life in fires, integral fire risks, fire automatics, residential real estate insurance.
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Ettore D’Ortona, Nicolino, and Maria Sole Staffa. "The theoretical surrender value in life insurance." Insurance Markets and Companies 7, no. 1 (November 18, 2016): 31–44. http://dx.doi.org/10.21511/imc.7(1).2016.04.
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In the context of the stochastic models for the management of life insurance portfolio, the authors explore, with simulation approach, the effects induced by the application of a particular method of calculation of the surrender value. In the life insurance, the policyholder position is, at any moment, quantified by the mathematical reserve. In case the reserve amount results are positive, the insurance company can allow the contract surrender, consisting in an amount payment, called surrender value, commensurate with the mathematical reserve. Generally, the insurance company enforces some restrictions in the surrender value determination, in order to avoid, first of all, that an amount is disbursed to the policyholder while, on the contrary, he results to be indebted to the Company. In this paper the authors will consider a surrender value calculation method based precisely on the profit recovery concept which shall be supplied by the contract in case it remains in the portfolio. Additionally, the authors shall analyze, by simulation approach, the effects caused by the enforcement of the surrender value calculation concept on a life portfolio profitability, and on the penalties extent enforced to the policyholders which cancel from the contract. Keywords: surrender value, life insurance, internal risk model, stochastic simulation
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Khare, S., A. Bonazzi, C. Mitas, and S. Jewson. "A framework for modeling clustering in natural hazard catastrophe risk management and the implications for re/insurance loss perspectives." Natural Hazards and Earth System Sciences Discussions 2, no. 8 (August 20, 2014): 5247–85. http://dx.doi.org/10.5194/nhessd-2-5247-2014.
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Abstract. In this paper, we present a novel framework for modelling clustering in natural hazard risk models. The framework we present is founded on physical principles where large-scale oscillations in the physical system is the source of non-Poissonian (clustered) frequency behaviour. We focus on a particular mathematical implementation of the "Super-Cluster" methodology that we introduce. This mathematical framework has a number of advantages including tunability to the problem at hand, as well as the ability to model cross-event correlation. Using European windstorm data as an example, we provide evidence that historical data show strong evidence of clustering. We then develop Poisson and clustered simulation models for the data, demonstrating clearly the superiority of the clustered model which we have implemented using the Poisson-Mixtures approach. We then discuss the implications of including clustering in models of prices on catXL contracts, one of the most commonly used mechanisms for transferring risk between primary insurers and reinsurers. This paper provides a number of new insights into the impact clustering has on modelled catXL contract prices. The simple model presented in this paper provides an insightful starting point for practicioners of natural hazard risk modelling.
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Embrechts, Paul, and Hanspeter Schmidli. "Ruin estimation for a general insurance risk model." Advances in Applied Probability 26, no. 02 (June 1994): 404–22. http://dx.doi.org/10.1017/s0001867800026264.
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Butuzov, S. Yu, A. V. Kryuchkov, and E. B. Tyutikova. "Safety management of tourist services based on insurance risk assessment." Technology of technosphere safety 90 (2020): 102–15. http://dx.doi.org/10.25257/tts.2020.4.90.102-115.
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Introduction. Employees of Emercom of Russia often participate in extreme tourism during their vacations, which helps to maintain their professional physical fitness. They are also attracted to help tourist groups that find themselves in a difficult situation in nature in a particular destination. Participation in extreme tourism is associated with the risk of injury. A general approach to the assessment of the impact of the management of the safety of tourist services in the instances associated with extreme tourism on insurance risks is presented. The purpose of the article is to create models for assessing the risks of extreme recreation. To do this, it is necessary to analyze the routes of extreme recreation in destinations from a mathematical point of view, and, based on this, to propose a number of management measures related, among other things, to insurance. Research methods are based on the use of the theory of discrete mathematics in the construction of a weighted graph describing the risks on the routes of tourists. The model allows us to quantify the risks on individual routes and, therefore, to build a target criterion for supporting the management of the safety of services in extreme tourism in a particular destination. Results and discussion. Building a graph of the route of a tourist group allows you to identify the least dangerous routes of tourist groups. This approach allows insurance companies to solve the problem of calculating the optimal and adequate amount of payments in the event of an insured event, as well as to reduce uncertainty in the actions of rescue units of Emercom of Russia. Conclusions. The methods of managing the safety of providing tourist services presented in the article reduce the probability of an insured event. Key words: insurance risk assessment, management of tourist services, tourist safety, security methods.
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Ghosh, Indranil, and Filipe J. Marques. "Tail Conditional Expectations Based on Kumaraswamy Dispersion Models." Mathematics 9, no. 13 (June 24, 2021): 1478. http://dx.doi.org/10.3390/math9131478.
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Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in housing development, and financial institutions offering loans to small-scale industries. Companies typically face three types of risk (and associated losses from each of these sources): strategic (S); operational (O); and financial (F) (insurance companies additionally face insurance risks) and they come from multiple sources. For asymmetric and bounded losses (properly adjusted as necessary) that are continuous in nature, we conjecture that risk assessment measures via univariate/bivariate Kumaraswamy distribution will be efficient in the sense that the resulting TCE based on bivariate Kumaraswamy type copulas do not depend on the marginals. In fact, almost all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copula’s domain of definition. In this article, we examined the above risk measure in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas. For illustrative purposes, a well-known Stock indices data set was re-analyzed by computing TCE for the bivariate KW type copulas to determine which pairs produce minimum risk in a two-component risk scenario.
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Ōsawa, Hideo. "Reversibility of Markov chains with applications to storage models." Journal of Applied Probability 22, no. 1 (March 1985): 123–37. http://dx.doi.org/10.2307/3213752.
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This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.
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Mare, Codruţa, Daniela Manaţe, Gabriela-Mihaela Mureşan, Simona Laura Dragoş, Cristian Mihai Dragoş, and Alexandra-Anca Purcel. "Machine Learning Models for Predicting Romanian Farmers’ Purchase of Crop Insurance." Mathematics 10, no. 19 (October 3, 2022): 3625. http://dx.doi.org/10.3390/math10193625.
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Considering the large size of the agricultural sector in Romania, increasing the crop insurance adoption rate and identifying the factors that drive adoption can present a real interest in the Romanian market. The main objective of this research was to identify the performance of machine learning (ML) models in predicting Romanian farmers’ purchase of crop insurance based on crop-level and farmer-level characteristics. The data set used contains 721 responses to a survey administered to Romanian farmers in September 2021, and includes both characteristics related to the crop as well as farmer-level socio-demographic attributes, perception about risk, perception about insurers and knowledge about agricultural insurance. Various ML algorithms have been implemented, and among the approaches developed, the Multi-Layer Perceptron Classifier (MLP) and the Linear Support Vector Classifier (SVC) outperform the other algorithms in terms of overall accuracy. Tree-based ensembles were used to identify the most prominent features, which included the farmer’s general perception of risk, their likelihood of engaging in risky behaviour, as well as their level of knowledge about crop insurance. The models implemented in this study could be a useful tool for insurers and policymakers for predicting potential crop insurance ownership.
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Taksar, Michael I. "Optimal risk and dividend distribution control models for an insurance company." Mathematical Methods of Operations Research (ZOR) 51, no. 1 (February 17, 2000): 1–42. http://dx.doi.org/10.1007/s001860050001.
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Rivas-Lopez, Maria Victoria, Roman Minguez-Salido, Mariano Matilla Garcia, and Alejandro Echeverria Rey. "Contributions from Spatial Models to Non-Life Insurance Pricing: An Empirical Application to Water Damage Risk." Mathematics 9, no. 19 (October 3, 2021): 2476. http://dx.doi.org/10.3390/math9192476.
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This paper explores the application of spatial models to non-life insurance data focused on the multi-risk home insurance branch. In the pricing modelling and rating process, spatial information should be considered by actuaries and insurance managers because frequencies and claim sizes may vary by region and the premium should be different considering this rating variable. In addition, it is relevant to examine the spatial dependence due to the fact that the frequency of claims in neighbouring regions is often expected to be more closely related than those in regions far from each other. In this paper, a comparison between spatial models, such as spatial autoregressive models (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM), and a non-spatial model has been developed. The data used for this analysis are for a home insurance portfolio located in Spain, from which we have selected peril of water coverage.
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Bäuerle, Nicole, and Rudolf Grübel. "Multivariate risk processes with interacting intensities." Advances in Applied Probability 40, no. 2 (June 2008): 578–601. http://dx.doi.org/10.1239/aap/1214950217.
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The classical models in risk theory consider a single type of claim. In the insurance business, however, several business lines with separate claim arrival processes appear naturally, and the individual claim processes may not be independent. We introduce a new class of models for such situations, where the underlying counting process is a multivariate continuous-time Markov chain of pure-birth type and the dependency of the components arises from the fact that the birth rate for a specific claim type may depend on the number of claims in the other component processes. Under certain conditions, we obtain a fluid limit, i.e. a functional law of large numbers for these processes. We also investigate the consequences of such results for questions of interest in insurance applications. Several specific subclasses of the general model are discussed in detail and the Cramér asymptotics of the ruin probabilities are derived in particular cases.
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Yuanjiang, He, Li Xucheng, and John Zhang. "Some results of ruin probability for the classical risk process." Journal of Applied Mathematics and Decision Sciences 7, no. 3 (January 1, 2003): 133–46. http://dx.doi.org/10.1155/s1173912603000130.
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The computation of ruin probability is an important problem in the collective risk theory. It has applications in the fields of insurance, actuarial science, and economics. Many mathematical models have been introduced to simulate business activities and ruin probability is studied based on these models. Two of these models are the classical risk model and the Cox model. In the classical model, the counting process is a Poisson process and in the Cox model, the counting process is a Cox process. Thorin (1973) studied the ruin probability based on the classical model with the assumption that random sequence followed the Γ distribution with density function f(x)=x1β−1β1βΓ(1/β)e−xβ, x>0, where β>1. This paper studies the ruin probability of the classical model where the random sequence follows the Γ distribution with density function f(x)=αnΓ(n)xn−1e−αx, x>0, where α>0 and n≥2 is a positive integer. An intermediate general result is given and a complete solution is provided for n=2. Simulation studies for the case of n=2 is also provided.
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Atoyev, Konstantin, and Pavel Knopov. "Assessment of Environmental, Social, Governance and Technogenic Components of Investment Risks." Cybernetics and Computer Technologies, no. 3 (November 29, 2022): 37–45. http://dx.doi.org/10.34229/2707-451x.22.3.4.
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Introduction. To assess the investment attractiveness (IA) and development opportunities for investment objects (IO), non-financial factors characterizing the environmental, social, governance and technogenic (ESGT) features of objects of possible financing have been increasingly used recently. The purpose of this data analysis is to establish how the ESGT-parameters of IO may reflect their financial health and performance prospects in a rapidly changing world. Having built an ESGT risk profile with the help of mathematical models, the IA of the object of study and the strategy of practical measures to increase it are determined. When modeling these processes, one should consider the growing uncertainty of the modern world due to the emergence of new risks; a large number of systemic links between the structures of the modern technosphere; the power-law nature of the distribution of the probability density of catastrophe damage, which decreases more slowly than the Gaussian dependence. In addition, the efficiency of complex production systems is largely determined by the balance of their individual links. Therefore, to assess investment risks, new methods are required to formalize the dependence of IA on ESGT-factors for the integrated management of the level of credit, market, insurance and operational risks under conditions of uncertainty. The purpose of the article is to develop mathematical methods for quantifying IA and determining real costs to improve the management, social and technological structure of IO, and minimize environmental pollution. Results. A mathematical model has been developed for assessing the environmental, social, managerial and technogenic leaving risks of investment, which makes it possible to determine the optimal strategies for increasing the IA of a possible IO. For a comprehensive risk assessment, methods of the theory of singularities of smooth reflections (TOGO) and the method of analysis of hierarchies (MAH) are used. The following algorithm for estimating IA is proposed: 1) determining the indices of the ESGT-components of risk; 2) calculation of bifurcation index values; 3) determination of the weakest links, which are associated with a decrease in IA; 4) identification of priority measures to prevent the reduction of IA or restore it to a predetermined level and minimize the negative impacts of extreme events and ensure sustainable development. Conclusions. The obtained results show that mathematical models based on the use of TOGO and MAH methods are an important tool for estimating IA under conditions of uncertainty. They allow: 1) to calculate the degree of approximation of the parameters characterizing the functioning of the object to their critical values ??when the IA changes; 2) to determine effective controls to minimize the risk of losing IA or minimize the time and losses for returning IA; 3) to consider the uncertainty factor associated with the features of the decision-making process. The development of this work is aimed at creating an information system for assessing IA for the integrated management of the level of credit, market, insurance and operational risks in the face of uncertainty and determining effective scenarios for minimizing investment risks. Keywords: mathematical modeling, system analysis, investment risks.
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Gasparian, Mikhail Samuilovich, Irina Anatolievna Kiseleva, Valery Alexandrovich Titov, and Natalia Alekseevna Sadovnikova. "St. Petersburg paradox: adoption of decisions on the basis of data mining and development of software in the sphere of business analytics." Nexo Revista Científica 34, no. 04 (October 28, 2021): 1370–80. http://dx.doi.org/10.5377/nexo.v34i04.12676.
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This article is devoted to analysis of models of St. Petersburg paradox, as well as development of software in the sphere of business analysis. This work is based on mathematical models using theories of probability and games as well as expert survey method. It is demonstrated that the St. Petersburg paradox is a mathematical problem of probability theory with artificial conditions. The influence of this problem on economical theory is exemplified by such provisions as the principle of diminishing marginal utility, the use of expected utility as criterion of decision adoption in uncertain environment, as well as foundations of microeconomics of insurance and risk management, theory of games and some approaches to financial simulation. Adoption of decisions on the basis of the St. Petersburg paradox is analyzed. Review of main decisions of the St. Petersburg paradox and their influence for economic theory has confirmed that the St. Petersburg paradox as a mathematical problem can be used as mathematical model upon implementation of financial simulation. Comparative analysis of available BI solutions has confirmed that most of them propose all major functions, and significant differences can be revealed in penetration of expanded functions.
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Li, Jingwei, Guoxin Liu, and Jinyan Zhao. "Optimal Dividend-Penalty Strategies for Insurance Risk Models with Surplus-Dependent Premiums." Acta Mathematica Scientia 40, no. 1 (December 17, 2019): 170–98. http://dx.doi.org/10.1007/s10473-020-0112-1.
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Wang, Shijie, and Wensheng Wang. "Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models." Journal of Applied Probability 44, no. 4 (December 2007): 889–900. http://dx.doi.org/10.1239/jap/1197908812.
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Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij, j ≥ 1}, i = 1,…,k. In this paper we investigate large deviations for both partial sums S(k; n1,…,nk) = ∑i=1k ∑j=1niXij and random sums S(k; t) = ∑i=1k ∑j=1Ni (t)Xij, where Ni(t), i = 1,…,k, are counting processes for the claim number. The obtained results extend some related classical results.
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Lee, Jen-Chieh, and Tyrone T. Lin. "Decision Analysis on Sustainable Value: Comparison of the London and Taiwan Markets for Product Integration of Family Security Services and Residential Fire Insurance." Journal of Risk and Financial Management 13, no. 11 (October 30, 2020): 266. http://dx.doi.org/10.3390/jrfm13110266.
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This paper explores a decision analysis on product integration of family security services and residential fire insurance in the London and Taiwan markets by using the proposed mathematical models for counting sustainable value. This paper shows the five main different results between London and Taiwan markets with ten different parameters of the family security market, to find out the optimal number of family security integrated services for each security company in London. The improvement of the risk aversion effect based on risk and financial management will enhance the market share of the private security industries in the London and Taiwan markets. The results of this research can serve as a reference for the decision-making of private security industries on product integration under sustainable value consideration. The research findings highlight the potential benefits for both the private security industry and the insurance industry in their design and negotiation for product integration to improve both of business operation and achieve corporate social responsibility goals to match the sustainability in the future.
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Lefèvre, Claude, and Matthieu Simon. "Ruin problems for epidemic insurance." Advances in Applied Probability 53, no. 2 (June 2021): 484–509. http://dx.doi.org/10.1017/apr.2020.66.
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AbstractThe paper discusses the risk of ruin in insurance coverage of an epidemic in a closed population. The model studied is an extended susceptible–infective–removed (SIR) epidemic model built by Lefèvre and Simon (Methodology Comput. Appl. Prob.22, 2020) as a block-structured Markov process. A fluid component is then introduced to describe the premium amounts received and the care costs reimbursed by the insurance. Our interest is in the risk of collapse of the corresponding reserves of the company. The use of matrix-analytic methods allows us to determine the distribution of ruin time, the probability of ruin, and the final amount of reserves. The case where the reserves are subjected to a Brownian noise is also studied. Finally, some of the results obtained are illustrated for two particular standard SIR epidemic models.
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Badescu, Andrei L., Eric C. K. Cheung, and David Landriault. "Dependent Risk Models with Bivariate Phase-Type Distributions." Journal of Applied Probability 46, no. 1 (March 2009): 113–31. http://dx.doi.org/10.1239/jap/1238592120.
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In this paper we consider an extension of the Sparre Andersen insurance risk model by relaxing one of its independence assumptions. The newly proposed dependence structure is introduced through the premise that the joint distribution of the interclaim time and the subsequent claim size is bivariate phase-type (see, e.g. Assaf et al. (1984) and Kulkarni (1989)). Relying on the existing connection between risk processes and fluid flows (see, e.g. Badescu et al. (2005), Badescu, Drekic and Landriault (2007), Ramaswami (2006), and Ahn, Badescu and Ramaswami (2007)), we construct an analytically tractable fluid flow that leads to the analysis of various ruin-related quantities in the aforementioned risk model. Using matrix-analytic methods, we obtain an explicit expression for the Gerber–Shiu discounted penalty function (see Gerber and Shiu (1998)) when the penalty function depends on the deficit at ruin only. Finally, we investigate how some ruin-related quantities involving the surplus immediately prior to ruin can also be analyzed via our fluid flow methodology.
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Levenchuk, Liudmyla. "The Bayesian approach to analysis of financial operational risk." ScienceRise, no. 2 (April 30, 2022): 11–20. http://dx.doi.org/10.21303/2313-8416.2022.002377.
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The article provides a short overview of methods for constructing mathematical models in the form of Bayesian Networks for modeling operational risks under conditions of uncertainty. Let’s provide the sequence of actions necessary for creating a model in the form of the network, methods for computing a probabilistic output in BN, and give examples of using the tool to solve practical problems of operational financial risk estimation. The study results can be used by financial institutions as a tool for resolving specific practical issues of risk estimation.
The object of research: methods for constructing Bayesian Networks for modeling operational risk in financial institutions.
Investigated problem: modeling operational risk under conditions of uncertainty.
The main scientific results: overview of methods for constructing Bayesian Networks for modeling operational risk under conditions of uncertainty; the methodology in the form of sequence of actions necessary for creating the model in the form of the network; methods for computing a probabilistic output in BN; examples of applying such approaches to solve practical problems of operational financial risk estimation.
The area of practical use of the research results: The research results can be used in the following financial institutions: banking system, insurance and investment companies.
Innovative technological product: computer based decision support system, allowing for high quality modeling and estimation of operational risks.
Scope of the innovative technological product: the practice of usage the proposed models in financial organizations provides an evidence of their high efficiency in terms of formal description and estimation of operational risk
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Michna, Zbigniew. "Self-similar processes in collective risk theory." Journal of Applied Mathematics and Stochastic Analysis 11, no. 4 (January 1, 1998): 429–48. http://dx.doi.org/10.1155/s1048953398000367.
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Collective risk theory is concerned with random fluctuations of the total assets and the risk reserve of an insurance company. In this paper we consider self-similar, continuous processes with stationary increments for the renewal model in risk theory. We construct a risk model which shows a mechanism of long range dependence of claims. We approximate the risk process by a self similar process with drift. The ruin probability within finite time is estimated for fractional Brownian motion with drift. A similar model is applicable in queueing systems, describing long range dependence in on/off processes and associated fluid models. The obtained results are useful in communication network models, as well as storage and inventory models.
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Alanzi, Ayed R. A., M. Qaisar Rafique, M. H. Tahir, Waqas Sami, and Farrukh Jamal. "A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications." Journal of Mathematics 2022 (December 31, 2022): 1–18. http://dx.doi.org/10.1155/2022/4288286.
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In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is done via the maximum likelihood estimation method. In order to show the usefulness of the proposed model, some well-established actuarial measures such as value-at-risk, expected-shortfall, tail-value-at-risk, tail-variance, and tail-variance-premium are obtained. A simulation study is carried out to assess the performance of maximum likelihood estimates. The empirical analysis is carried out to show that our proposed model is better in performance as compared to other competitive models related to the extended Kumaraswamy model. Thus, insurance claim data and engineering related real-life data sets are considered to prove this claim.
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Kalfin, Kalfin, Sukono Sukono, Sudradjat Supian, and Mustafa Mamat. "Insurance Premium Determination Model and Innovation for Economic Recovery Due to Natural Disasters in Indonesia." Computation 10, no. 10 (September 28, 2022): 174. http://dx.doi.org/10.3390/computation10100174.
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Climate change that occurs causes the risk of natural disasters to continue to increase throughout the world. Economic losses are unavoidable, leading to the need for continuous innovation in post-disaster economic recovery efforts. Insurance is one of the offers in providing funding for the economic recovery that occurs. This study aimed to develop innovations and models for determining natural disaster insurance premiums with a subsidy and tax system. In addition, the developed model considers the disaster risk index in the form of the level of risk distribution, the frequency of events, and economic losses. In this study, the data used were the frequency of events and economic losses obtained from the Indonesian National Disaster Management Agency. The data used were 20 database periods from 2000 to 2019. This study used the collective risk method from the index of natural disaster risk parameters. From the results of the analysis, it was found that the level of distribution of disaster risk affected the determination of insurance premiums. The amount of insurance premiums is increasing along with the increase in the magnitude of the spread of disaster risk. In addition, if taxes and subsidies are reduced, then for high-risk areas, there will be a decrease in the burden of insurance premiums, and for low-risk areas, there will be an increase in the premium burden that must be paid. On the basis of the results of the analysis on the insurance model, it was found that the insurance premiums in each province varied. The results of this study are expected to be a reference for the government and private companies in implementing disaster insurance in Indonesia. In addition, the results of this study can be a means of developing innovations for disaster risk management that occurs.
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Albrecher, Hansjörg, Sem C. Borst, Onno J. Boxma, and Jacques Resing. "Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models." Journal of Applied Probability 48, A (August 2011): 3–14. http://dx.doi.org/10.1017/s0021900200099083.
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In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramér–Lundberg model with and without tax payments. We also provide a relation of the Cramér–Lundberg risk model with the G/G/∞ queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramér– Lundberg risk model.
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Ryan, Gearóid. "Hedging your bets in a volatile world: an introduction to the use and pricing of European call options." Boolean: Snapshots of Doctoral Research at University College Cork, no. 2011 (January 1, 2011): 207–10. http://dx.doi.org/10.33178/boolean.2011.43.
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In recent years, our economy and livelihoods have been affected by the volatility of financial markets. We have seen how banks and investors have failed to control and understand their risks. In this article, I outline one of the fundamental tools used to control exposure to risk in financial markets. In doing so, I explore some of the underlying assumptions of mathematical models used in the financial industry today and show how my research attempts to make these assumptions more realistic while keeping the model simple. As well as the trading of stocks and shares, many of the transactions in financial markets consist of the trading of contracts. Such a contract may be an agreement between two parties on the price of a stock, the quantity and time of delivery of some commodity, or contracts that provide insurance for investors. My research is concerned with determining the value of one ...
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Krah, Anne-Sophie, Zoran Nikolić, and Ralf Korn. "Least-Squares Monte Carlo for Proxy Modeling in Life Insurance: Neural Networks." Risks 8, no. 4 (November 4, 2020): 116. http://dx.doi.org/10.3390/risks8040116.
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The least-squares Monte Carlo method has proved to be a suitable approximation technique for the calculation of a life insurer’s solvency capital requirements. We suggest to enhance it by the use of a neural network based approach to construct the proxy function that models the insurer’s loss with respect to the risk factors the insurance business is exposed to. After giving a mathematical introduction to feed forward neural networks and describing the involved hyperparameters, we apply this popular form of neural networks to a slightly disguised data set from a German life insurer. Thereby, we demonstrate all practical aspects, such as the hyperparameter choice, to obtain our candidate neural networks by bruteforce, the calibration (“training”) and validation (“testing”) of the neural networks and judging their approximation performance. Compared to adaptive OLS, GLM, GAM and FGLS regression approaches, an ensemble built of the 10 best derived neural networks shows an excellent performance. Through a comparison with the results obtained by every single neural network, we point out the significance of the ensemble-based approach. Lastly, we comment on the interpretability of neural networks compared to polynomials for sensitivity analyses.
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Donnelly, Catherine, and Paul Embrechts. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis." ASTIN Bulletin 40, no. 1 (May 2010): 1–33. http://dx.doi.org/10.2143/ast.40.1.2049222.
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AbstractIn the aftermath of the 2007-2008 financial crisis, there has been criticism of mathematics and the mathematical models used by the finance industry. We answer these criticisms through a discussion of some of the actuarial models used in the pricing of credit derivatives. As an example, we focus in particular on the Gaussian copula model and its drawbacks. To put this discussion into its proper context, we give a synopsis of the financial crisis and a brief introduction to some of the common credit derivatives and highlight the difficulties in valuing some of them.We also take a closer look at the risk management issues in part of the insurance industry that came to light during the financial crisis. As a backdrop to this, we recount the events that took place at American International Group during the financial crisis. Finally, through our paper we hope to bring to the attention of a broad actuarial readership some “lessons (to be) learned” or “events not to be forgotten”.
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Khalfallah, Mohammed El-arbi, Mohammed Lakhdar Hadji, and Josep Vives. "Pricing cumulative loss derivatives under additive models via Malliavin calculus." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–15. http://dx.doi.org/10.5269/bspm.51549.
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We show that integration by parts formulas based on Malliavin-Skorohod calculus techniques for additive processes help us to compute quantities like ${\E}(L_T h(L_T))$ for different suitable functions $h$ and different models for the cumulative loss process $L_T$. These quantities are important in Insurance and Finance. For example they appear in computing expected shortfall risk measures or stop-loss contracts. The formulas given in the present paper, obtained by simple proofs, generalize the formulas given in a recent paper by Hillairet, Jiao and Réveillac using Malliavin calculus techniques for the standard Poisson process, a particular case of additive process.
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Hürlimann, Werner. "Economic capital modelling for the MTPL man-made catastrophe risk." Annals of Actuarial Science 7, no. 1 (September 4, 2012): 46–60. http://dx.doi.org/10.1017/s1748499512000164.
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AbstractWe undertake a mathematical clarification of the QIS5 proposal for the calculation of the Motor Third Party Liability (MTPL) man-made catastrophe risk capital in terms of two more general models. The QIS5 model assumption implies that the total loss consists of a single catastrophe claim in case it occurs during the next one-year insurance time period. However, the total loss should instead be dynamically modelled by a sequence of claims of varying size that follow a compound Poisson Pareto model, which is our first alternative model. A second possibility also takes into account the effect of investments, whose financial return process follows a Black-Scholes-Merton model. If one excludes limits of coverage, then asymptotically as the total loss increases without limits the first model is equivalent to the model assumption obtained from the QIS5 assumption by replacing a single catastrophe claim by the total loss. In other words, the QIS5 simple model is justified as limiting asymptotic approximation to the classical compound Poisson Pareto model. Conversely, an asymptotic approximation to the VaR economic capital from this model identifies with a modified QIS5 CAT formula. The inclusion of limits of coverage is also analyzed. In this situation we obtain new simple closed-form implementations of the economic capital formulas.
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Gajek, Lesław, and Marcin Rudź. "Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model." Methodology and Computing in Applied Probability 22, no. 4 (March 26, 2018): 1493–506. http://dx.doi.org/10.1007/s11009-018-9627-2.
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AbstractAfter implementation of Solvency II, insurance companies can use internal risk models. In this paper, we show how to calculate finite-horizon ruin probabilities and prove for them new upper and lower bounds in a risk-switching Sparre Andersen model. Due to its flexibility, the model can be helpful for calculating some regulatory capital requirements. The model generalizes several discrete time- as well as continuous time risk models. A Markov chain is used as a ‘switch’ changing the amount and/or respective wait time distributions of claims while the insurer can adapt the premiums in response. The envelopes of generalized moment generating functions are applied to bound insurer’s ruin probabilities.
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Ryzhkov, O. Yu, and V. V. Glinskiy. "Risk Evaluation Using the Theory of Generalized Actuarial Calculations." Voprosy statistiki 26, no. 2 (March 9, 2019): 18–26. http://dx.doi.org/10.34023/2313-6383-2019-26-2-18-26.
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The article is prepared based on the results of theoretical studies conducted by the authors in the field of actuarial calculations, the improvement of which is one of the development directions for statistical science.In modern economic conditions, the assessment of risks inherent in economic entities in all spheres of activity and leading to significant losses, such as credit, operational risk, liquidity risk, and so forth is of particular importance. Quantitative assessment of the level of risks is the subject of actuarial calculations. However, the existing apparatus of actuarial science is mainly focused on solving specific issues facing the insurance industry (including pension insurance) and is not adapted to assess the level of risk.The article presents the key positions of the author’s theory of actuarial calculations, which offers a generalized approach to solving actuarial problems in various types of economic activities using a variety of information about the risk. The basic idea of the theory is that any result of actuarial calculations can be expressed in terms of quantiles of the future net loss associated with the realization of risk.The estimation of each quantile can be considered as a special case of evaluation of unobserved economic values, such as cost, projected profit, and so forth. The problem of estimating these values lies with the multivariance of the original data and methods, as a result of which different specialists often receive significantly divergent estimates.For this, the author proposed to use the methodology of evaluation, which consists in obtaining the median of all single estimates that can be obtained from representative samples of possible scenarios, evaluation models and values of the original data. This methodology can be used to estimate the quantiles of the future loss, and the complexity of the original data involves the use of numerical methods, in particular, the Monte Carlo method.The authors tested research tools on the example of solving the problem of quantitative characteristic of credit risk. They also constructed and estimated the mathematical and statistical model of loss from the default of the borrower, and proved the possibility of sufficient repeatability and reproducibility of results. The data of state statistics, financial statements of credit institutions, model estimates served as initial data.
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Ferreiro, Ana M., Enrico Ferri, José A. García, and Carlos Vázquez. "Global Optimization for Automatic Model Points Selection in Life Insurance Portfolios." Mathematics 9, no. 5 (February 25, 2021): 472. http://dx.doi.org/10.3390/math9050472.
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Starting from an original portfolio of life insurance policies, in this article we propose a methodology to select model points portfolios that reproduce the original one, preserving its market risk under a certain measure. In order to achieve this goal, we first define an appropriate risk functional that measures the market risk associated to the interest rates evolution. Although other alternative interest rate models could be considered, we have chosen the LIBOR (London Interbank Offered Rate) market model. Once we have selected the proper risk functional, the problem of finding the model points of the replicating portfolio is formulated as a problem of minimizing the distance between the original and the target model points portfolios, under the measure given by the proposed risk functional. In this way, a high-dimensional global optimization problem arises and a suitable hybrid global optimization algorithm is proposed for the efficient solution of this problem. Some examples illustrate the performance of a parallel multi-CPU implementation for the evaluation of the risk functional, as well as the efficiency of the hybrid Basin Hopping optimization algorithm to obtain the model points portfolio.
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Perera, S. S. N. "Analysis of Economic Burden of Seasonal Influenza: An Actuarial Based Conceptual Model." Journal of Applied Mathematics 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/4264737.
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Analysing the economic burden of the seasonal influenza is highly essential due to the large number of outbreaks in recent years. Mathematical and actuarial models can be considered as management tools to understand the dynamical behavior, predict the risk, and compute it. This study is an attempt to develop conceptual model to investigate the economic burden due to seasonal influenza. The compartment SIS (susceptible-infected-susceptible) model is used to capture the dynamical behavior of influenza. Considering the current investment and future medical care expenditure as premium payment and benefit (claim), respectively, the insurance and actuarial based conceptual model is proposed to model the present economic burden due to the spread of influenza. Simulation is carried out to demonstrate the variation of the present economic burden with respect to model parameters. The sensitivity of the present economic burden is studied with respect to the risk of disease spread. The basic reproduction is used to identify the risk of disease spread. Impact of the seasonality is studied by introducing the seasonally varying infection rate. The proposed model provides theoretical background to investigate the economic burden of seasonal influenza.
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Pfeifer, Dietmar, and Olena Ragulina. "Generating unfavourable VaR scenarios under Solvency II with patchwork copulas." Dependence Modeling 9, no. 1 (January 1, 2021): 327–46. http://dx.doi.org/10.1515/demo-2021-0115.
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Abstract The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the European Union. Besides this, the Delegated Regulation by the European Commission requires all insurance companies under supervision to consider different risk scenarios in their risk management system for the company’s own risk assessment. Since it is unreasonable to assume that the potential worst case scenario will materialize in the company, we think that a modelling of various unfavourable scenarios as described in this paper is likewise appropriate. Our explicit copula approach can be considered as a special case of ordinal sums, which in two dimensions even leads to the technically worst VaR scenario.
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Xie, Shengkun, and Rebecca Luo. "Measuring Variable Importance in Generalized Linear Models for Modeling Size of Loss Distributions." Mathematics 10, no. 10 (May 11, 2022): 1630. http://dx.doi.org/10.3390/math10101630.
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Predictive modeling is a critical technique in many real-world applications, including auto insurance rate-making and the decision making of rate filings review for regulation purposes. It is also important in predicting financial and economic risk in business and economics. Unlike testing hypotheses in statistical inference, results obtained from predictive modeling serve as statistical evidence for the decision making of the underlying problem and discovering the functional relationship between the response variable and the predictors. As a result of this, the variable importance measures become an essential aspect of helping to better understand the contributions of predictors to the built model. In this work, we focus on the study of using generalized linear models (GLM) for the size of loss distributions. In addition, we address the problem of measuring the importance of the variables used in the GLM to further evaluate their potential impact on insurance pricing. In this regard, we propose to shift the focus from variable importance measures of factor levels to factors themselves and to develop variable importance measures for factors included in the model. Therefore, this work is exclusively for modeling with categorical variables as predictors. This work contributes to the further development of GLM modeling to make it even more practical due to this added value. This study also aims to provide benchmark estimates to allow for the regulation of insurance rates using GLM from the variable importance aspect.
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Jin, Zhuo, Rebecca Stockbridge, and George Yin. "Some Recent Progress on Numerical Methods for Controlled Regime-Switching Models with Applications to Insurance and Risk Management." Computational Methods in Applied Mathematics 15, no. 3 (July 1, 2015): 331–51. http://dx.doi.org/10.1515/cmam-2015-0015.
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AbstractThis paper provides a survey on several numerical approximation schemes for stochastic control problems that arise from actuarial science and finance. The problems to be considered include dividend optimization, reinsurance game, and quantile hedging for guaranteed minimum death benefits. To better describe the complicated financial markets and their inherent uncertainty and randomness, the so-called regime-switching models are adopted. Such models are more realistic and versatile, however, far more complicated to handle. Due to the complexity of the construction, the regime-switching diffusion systems can only be solved in very special cases. In general, it is virtually impossible to obtain closed-form solutions. We use Markov chain approximation techniques to construct discrete-time controlled Markov chains to approximate the value function and optimal controls. Examples are presented to illustrate the applicability of the numerical methods.
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Lin, Peng, Martin Neil, and Norman Fenton. "Risk aggregation in the presence of discrete causally connected random variables." Annals of Actuarial Science 8, no. 2 (August 26, 2014): 298–319. http://dx.doi.org/10.1017/s1748499514000098.
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AbstractRisk aggregation is a popular method used to estimate the sum of a collection of financial assets or events, where each asset or event is modelled as a random variable. Applications include insurance, operational risk, stress testing and sensitivity analysis. In practice, the sum of a set of random variables involves the use of two well-known mathematical operations: n-fold convolution (for a fixed number n) and N-fold convolution, defined as the compound sum of a frequency distribution N and a severity distribution, where the number of constant n-fold convolutions is determined by N, where the severity and frequency variables are independent, and continuous, currently numerical solutions such as, Panjer’s recursion, fast Fourier transforms and Monte Carlo simulation produce acceptable results. However, they have not been designed to cope with new modelling challenges that require hybrid models containing discrete explanatory (regime switching) variables or where discrete and continuous variables are inter-dependent and may influence the severity and frequency in complex, non-linear, ways. This paper describes a Bayesian Factorisation and Elimination (BFE) algorithm that performs convolution on the hybrid models required to aggregate risk in the presence of causal dependencies. This algorithm exploits a number of advances from the field of Bayesian Networks, covering methods to approximate statistical and conditionally deterministic functions to factorise multivariate distributions for efficient computation. Experiments show that BFE is as accurate on conventional problems as competing methods. For more difficult hybrid problems BFE can provide a more general solution that the others cannot offer. In addition, the BFE approach can be easily extended to perform deconvolution for the purposes of stress testing and sensitivity analysis in a way that competing methods do not.
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Farina, Francesco, Stefania Ottone, and Ferruccio Ponzano. "On the Collective Choice among Models of Social Protection: An Experimental Study." Games 10, no. 4 (October 11, 2019): 41. http://dx.doi.org/10.3390/g10040041.
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A real-effort experiment is conducted in order to detect preferences for one out of three different models of the Welfare State characterized by different tax-and-transfer schemes. We reproduce a small society in the lab where: Subjects are grouped in three stylized classes (the rich, the middle class and the poor) on the basis of their performance in a real-effort activity; income and risk are assigned according to the class; tax revenue is spent to refund unlucky people and to provide a public good. Experimental subjects must choose (both under and without a veil of ignorance concerning their position in the society created in the lab) among (a) a baseline proportional scheme, where the State is neutral with respect to risk heterogeneity; (b) an actuarially fair scheme where low ability and low earnings subjects bear full individual responsibility for risk exposure and (c) a progressive scheme where mutual risk insurance spreads risk across all subjects such that low ability and low earnings individuals are compensated. Our most relevant finding is that preference is motivated less by a justice principle and more by self-interested considerations on the expectations surrounding one’s own position in the society.