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1
Frangos, Nicholas E., and Spyridon D. Vrontos. "Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance." ASTIN Bulletin 31, no. 1 (May 2001): 1–22. http://dx.doi.org/10.2143/ast.31.1.991.
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AbstractThe majority of optimal Bonus-Malus Systems (BMS) presented up to now in the actuarial literature assign to each policyholder a premium based on the number of his accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, we develop in this paper, the design of optimal BMS with both a frequency and a severity component. The optimal BMS designed are based both on the number of accidents of each policyholder and on the size of loss (severity) for each accident incurred. Optimality is obtained by minimizing the insurer's risk. Furthermore we incorporate in the above design of optimal BMS the important a priori information we have for each policyholder. Thus we propose a generalised BMS that takes into consideration simultaneously the individual's characteristics, the number of his accidents and the exact level of severity for each accident.
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Braun, Alexander, Marius Fischer, and Hato Schmeiser. "How to derive optimal guarantee levels in participating life insurance contracts." Journal of Risk Finance 20, no. 5 (November 18, 2019): 445–69. http://dx.doi.org/10.1108/jrf-07-2018-0099.
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Purpose The purpose of this paper is to show how an insurance company can maximize the policyholder’s utility by setting the level of the interest rate guarantee in line with his preferences. Design/methodology/approach The authors develop a general model of life insurance, taking stochastic interest rates, early default and regular premium payments into account. Furthermore, the authors assume that equity holders must receive risk-adequate returns on their initial equity contribution and that the insurance company has to maintain a solvency restriction. Findings The findings show that the optimal level for the interest rate guarantee is in general far below the maximum value typically set by the supervisory authorities and insurance companies. Originality/value The authors conclude that the approach of deviating from the maximum interest rate guarantee level given by the regulatory requirements can create additional value for the rational policyholder. In contrast to Schmeiser and Wagner (2014), the second finding shows that the interest rate guarantee embedded in a life insurance product becomes less attractive compared to a pure investment in the underlying asset portfolio to the policyholder when the guarantee level is lowered too far or the contract duration is short. They also refute Schmeiser and Wagner (2014) by showing that the equity capital required by the insurance company increases with the level of the guarantee, even if the insurer is flexible with respect to its asset allocation. The last finding is that a policyholder with higher risk aversion does not generally prefer a higher guarantee level.
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Adisti, Rillifa Iris, and Aceng Komarudin Mutaqin. "PERHITUNGAN PREMI MURNI PADA SISTEM BONUS MALUS UNTUK FREKUENSI KLAIM BERDISTRIBUSI BINOMIAL NEGATIF DAN BESAR KLAIM BERDISTRIBUSI WEIBULL PADA DATA ASURANSI KENDARAAN BERMOTOR DI INDONESIA." Jurnal Gaussian 10, no. 2 (May 31, 2021): 170–79. http://dx.doi.org/10.14710/j.gauss.v10i2.30084.
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System bonus malus is one of the systems offered by an insurance company where the risk premium calculation is based on the claim history of each policyholder. In study will be discussed premium calculation in system, bonus malus where the frequency of claims has a negative binomial distribution and the size of claims is Weibull distribution on motor vehicle insurance data in Indonesia. This method will producesystem an bonus malus optimal by finding the posterior distribution using Bayes analysis. As the application material used secondary data from the recording results obtained from the general insurance company PT. XYZ in 2014, data contains data on the frequency of claims and the amount ofclaims partial loss of policyholders forinsurance products for comprehensivemotor vehicle insurance category 8 regions 3.The results of the implementation show that the premiums with the system are bonus malus optimalconsidered fair enough because the premiums paid by policyholders insurance that extends the policy in the following year is proportional to the risk it faces, where the premium to be paid by each policyholder is based on past claims history. Keywords: system bonus malus, negative binomial distribution, Weibull distribution, comprehensive, partial loss.
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Kalife, Aymeric, Gabriela López Ruiz, Saad Mouti, and Xiaolu Tan. "Optimal behavior strategy in the GMIB product." Insurance Markets and Companies 9, no. 1 (September 26, 2018): 41–69. http://dx.doi.org/10.21511/ins.09(1).2018.05.
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Guaranteed Minimum Income benefit are variable annuities contract, which offer the policyholder the possibility to con- vert the guarantee level into an annuities income for life. This paper focuses on the optimal customer behavior assuming the maximization of the discounted expected future cash flows over the full life of the contract duration. Using convenient scaling properties of the contract value enables to reduce the complexity (dimension) of the problem and to characterize the policyholder’s decision as a function of the contract moneyness across four main choices: zero withdrawals, guaranteed withdrawals, lapse and the income period election. Sensitivities to key drivers such as the market volatility, the interest rate and the roll-up rate illustrate how crucial are not only the environment, but also the product design features, in order to ensure a fair and robust pricing for both customer and life insurer. In particular, the authors find that most empirical contracts are usually underpriced compared to mean optimal behavior pricing, which empirically translated into multiple updates of behavior assumptions and re-reserving by life insurers in the recent years.
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Chen, An, Peter Hieber, and Jakob K. Klein. "TONUITY: A NOVEL INDIVIDUAL-ORIENTED RETIREMENT PLAN." ASTIN Bulletin 49, no. 1 (December 26, 2018): 5–30. http://dx.doi.org/10.1017/asb.2018.33.
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AbstractFor insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company’s role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder’s viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity’s payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder’s lifetime utility.
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Chen, An, and Peter Hieber. "OPTIMAL ASSET ALLOCATION IN LIFE INSURANCE: THE IMPACT OF REGULATION." ASTIN Bulletin 46, no. 3 (May 16, 2016): 605–26. http://dx.doi.org/10.1017/asb.2016.12.
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AbstractIn a typical equity-linked life insurance contract, the insurance company is entitled to a share of return surpluses as compensation for the return guarantee granted to the policyholders. The set of possible contract terms might, however, be restricted by a regulatory default constraint — a fact that can force the two parties to initiate sub-optimal insurance contracts. We show that this effect can be mitigated if regulatory policy is more flexible. We suggest that the regulator implement a traffic light system where companies are forced to reduce the riskiness of their asset allocation in distress. In a utility-based framework, we show that the introduction of such a system can increase the benefits of the policyholder without deteriorating the benefits of the insurance company. At the same time, default probabilities (and thus solvency capital requirements) can be reduced.
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Turgeon-Rhéaume, Maxime, and Van Son Lai. "Analyse d’impact du moment de décaissement d’un produit avec garantie de rachat viager." Assurances et gestion des risques 87, no. 3-4 (March 31, 2021): 131–68. http://dx.doi.org/10.7202/1076121ar.
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The extant literature on the Guaranteed Lifetime Withdrawal Benefits (GLWB) financial risk is abundant, however, few articles investigate the option offered to the policyholder with respect to the initiation of the contract and examine this impact on the profitability of the product for the insurer.
We extend the analysis carried out by Huang et al. (IME, 2014) on the optimal initiation of the product with GLWB. First, we add an additional dimension in the analysis to account for the insurer losses as a function of the age for disbursement chosen by the policyholder. Then, we develop a novel analytical framework to determine by numerical methods the extent to which an insurer, expecting his client to choose when to receive benefits to maximize the value of his variable annuity contract, should change its actuarially fair fee structure. We show that the fair premium is a function of the insured policyholder age when he bought the contract. This result runs counter to the current fee structure and practice in the Canadian insurance industry with insurers charging a uniform level of fees regardless of the policyholder biological age when the contract is issued.
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Golubin, A. Yu, and V. N. Gridin. "Optimal insurance strategies in a risk process with restrictions on policyholder risks." Automation and Remote Control 71, no. 8 (August 2010): 1578–89. http://dx.doi.org/10.1134/s0005117910080072.
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Lin, Jyh-Horng, Xuelian Li, and Fu-Wei Huang. "Insurer interest margin management, default risk, and life insurance policyholder protection." Journal of Modelling in Management 13, no. 3 (August 13, 2018): 718–35. http://dx.doi.org/10.1108/jm2-12-2017-0140.
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Purpose This paper aims to theoretically examine the effects of regulatory policyholder protection on spread behavior and default probability of a life insurance company. Design/methodology/approach The authors construct a contingent claim model for the valuation of the equity of a life insurance company. Then, they extend it to model default risk measures associated with a more appropriate behavioral mode of strategic invested asset rate-setting under regulation. Findings The findings established that the optimal insurer interest margin is explicitly modeled by a spread between the loan rate and the required guaranteed rate of the company. The effect of the guaranteed rate on the insurer interest margin is positive when the barrier is low, whereas it is negative when the barrier is high. As the barrier increases, the positive effect of the guaranteed rate on the default risk is increased, the negative effect of the participation on the insurer interest margin is decreased and the positive effect of the participation on the default risk is decreased. Practical implications Several results derived that should be of interest to investors, analysts, supervising agencies and policymakers. For example, policyholders protected by increasing the guaranteed rate may create a higher risk for the life insurance company to meet its obligations. Originality/value The authors’ approach is a significant departure from the existing literature; they differentiate among path-dependent, barrier options and suggest that the life insurance company’s defaults are more commonly triggered by regulatory responses than debt default.
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Bauer, Daniel, Alexander Kling, and Jochen Russ. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities." ASTIN Bulletin 38, no. 02 (November 2008): 621–51. http://dx.doi.org/10.2143/ast.38.2.2033356.
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Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.
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Bauer, Daniel, Alexander Kling, and Jochen Russ. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities." ASTIN Bulletin 38, no. 2 (November 2008): 621–51. http://dx.doi.org/10.1017/s0515036100015312.
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Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.
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MELNIKOV, ALEXANDER, and YULIYA ROMANYUK. "EFFICIENT HEDGING AND PRICING OF EQUITY-LINKED LIFE INSURANCE CONTRACTS ON SEVERAL RISKY ASSETS." International Journal of Theoretical and Applied Finance 11, no. 03 (May 2008): 295–323. http://dx.doi.org/10.1142/s0219024908004816.
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The paper uses the efficient hedging methodology in order to optimally price and hedge equity-linked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, we consider a policy which pays the maximum of the values of n risky assets at some maturity date T, provided that the policyholder survives to T. Such contracts incorporate financial risk, which stems from the uncertainty about future prices of the underlying financial assets, and insurance risk, which arises from the policyholder's mortality. We show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. We also prove a probabilistic result, which allows one to calculate analytic pricing formulas for equity-linked payoffs with n risky assets. To illustrate its use, explicit formulas are given for optimal prices and expected hedging losses for payoffs with two risky assets. Numerical examples highlighting the implications of efficient hedging for the management of financial and insurance risks of equity-linked life insurance policies are also provided.
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Tzougas, George, Spyridon Vrontos, and Nicholas Frangos. "OPTIMAL BONUS-MALUS SYSTEMS USING FINITE MIXTURE MODELS." ASTIN Bulletin 44, no. 2 (January 10, 2014): 417–44. http://dx.doi.org/10.1017/asb.2013.31.
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AbstractThis paper presents the design of optimal Bonus-Malus Systems using finite mixture models, extending the work of Lemaire (1995; Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Norwell, MA: Kluwer) and Frangos and Vrontos (2001; Frangos, N. and Vrontos, S. (2001) Design of optimal bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin, 31(1), 1–22). Specifically, for the frequency component we employ finite Poisson, Delaporte and Negative Binomial mixtures, while for the severity component we employ finite Exponential, Gamma, Weibull and Generalized Beta Type II mixtures, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized Bonus-Malus Systems we propose, integrate risk classification and experience rating by taking into account both the a priori and a posteriori characteristics of each policyholder.
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Moenig, Thorsten, and Daniel Bauer. "Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities *." Review of Finance 20, no. 2 (May 25, 2015): 759–94. http://dx.doi.org/10.1093/rof/rfv018.
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Chiarolla, Maria B., Tiziano De Angelis, and Gabriele Stabile. "An analytical study of participating policies with minimum rate guarantee and surrender option." Finance and Stochastics 26, no. 2 (January 28, 2022): 173–216. http://dx.doi.org/10.1007/s00780-022-00471-0.
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AbstractWe perform a detailed theoretical study of the value of a class of participating policies with four key features: (i) the policyholder is guaranteed a minimum interest rate on the policy reserve; (ii) the contract can be terminated by the holder at any time until maturity (surrender option); (iii) at the maturity (or upon surrender), a bonus is credited to the holder if the portfolio backing the policy outperforms the current policy reserve; (iv) due to solvency requirements, the contract ends if the value of the underlying portfolio of assets falls below the policy reserve.Our analysis is probabilistic and relies on optimal stopping and free boundary theory. We find a structure of the optimal surrender strategy which was undetected by previous (mostly numerical) studies on the topic. Optimal surrender of the contract is triggered by two ‘stop-loss’ boundaries and by a ‘too-good-to-persist’ boundary (in the language of Ekström and Vaicenavicius in Stoch. Process. Appl. 130: 806–823, 2020). Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.
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Aase, Knut K. "Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization." ASTIN Bulletin 23, no. 2 (November 1993): 185–211. http://dx.doi.org/10.2143/ast.23.2.2005091.
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AbstractThis paper attempts to give an overview of the pricing of risks in a pure exchange economy, where trade takes place at time zero and where uncertainty is revealed at time one. An economic equilibrium model under uncertainty is formulated, where conditions characterizing a Pareto optimal exchange equilibrium are derived. We present two sets of sufficient conditions for the existence of an equilibrium, and demonstrate how equilibria can be characterized through several examples. Uniqueness of equilibrium is also discussed. Special attention is given to the principal components that the premiums in a reinsurance market must depend upon. We also apply the general theory to the risk exchange problem between a policyholder and an insurer, and in particular we compute market premiums of the resulting optimal contracts.It is emphasized throughout how the formulation of a competitive equilibrium, rather than merely a general risk exchange formulation, is of particular interest in deriving a well-defined and unique set of equilibrium premiums in an insurance market. The theory is put into a framework which is fruitful for extensions beyond the one-period case.
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Luo, Xiaolin, and Pavel V. Shevchenko. "Fast numerical method for pricing of variable annuities with guaranteed minimum withdrawal benefit under optimal withdrawal strategy." International Journal of Financial Engineering 02, no. 03 (September 2015): 1550024. http://dx.doi.org/10.1142/s2424786315500243.
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A variable annuity contract with guaranteed minimum withdrawal benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with GMWB becomes an optimal stochastic control problem. So far in the literature these contracts have only been evaluated by solving partial differential equations (PDE) using the finite difference method. The well-known least-squares or similar Monte Carlo methods cannot be applied to pricing these contracts because the paths of the underlying wealth process are affected by optimal cash withdrawals (control variables) and thus cannot be simulated forward in time. In this paper, we present a very efficient new algorithm for pricing these contracts in the case when transition density of the underlying asset between withdrawal dates or its moments are known. This algorithm relies on computing the expected contract value through a high order Gauss–Hermite quadrature applied on a cubic spline interpolation. Numerical results from the new algorithm for a series of GMWB contract are then presented, in comparison with results using the finite difference method solving corresponding PDE. The comparison demonstrates that the new algorithm produces results in very close agreement with those of the finite difference method, but at the same time it is significantly faster; virtually instant results on a standard desktop PC.
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Alemany, Ramon, Catalina Bolancé, Roberto Rodrigo, and Raluca Vernic. "Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity." Mathematics 9, no. 1 (December 31, 2020): 73. http://dx.doi.org/10.3390/math9010073.
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The aim of this paper is to introduce dependence between the claim frequency and the average severity of a policyholder or of an insurance portfolio using a bivariate Sarmanov distribution, that allows to join variables of different types and with different distributions, thus being a good candidate for modeling the dependence between the two previously mentioned random variables. To model the claim frequency, a generalized linear model based on a mixed Poisson distribution -like for example, the Negative Binomial (NB), usually works. However, finding a distribution for the claim severity is not that easy. In practice, the Lognormal distribution fits well in many cases. Since the natural logarithm of a Lognormal variable is Normal distributed, this relation is generalised using the Box-Cox transformation to model the average claim severity. Therefore, we propose a bivariate Sarmanov model having as marginals a Negative Binomial and a Normal Generalized Linear Models (GLMs), also depending on the parameters of the Box-Cox transformation. We apply this model to the analysis of the frequency-severity bivariate distribution associated to a pay-as-you-drive motor insurance portfolio with explanatory telematic variables.
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Afonso, Lourdes B., Rui M. R. Cardoso, Alfredo D. Egídio dos Reis, and Gracinda Rita Guerreiro. "MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE." ASTIN Bulletin 47, no. 2 (March 21, 2017): 417–35. http://dx.doi.org/10.1017/asb.2017.3.
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AbstractMotor insurance is a very competitive business where insurers operate with quite large portfolios, often decisions must be taken under short horizons and therefore ruin probabilities should be calculated in finite time. The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramér–Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. Focusing on the classical model for bonus-malus systems, we propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or even between different bonus-malus rules. In our work, the required initial surplus can also be evaluated. We consider an application of a bonus-malus system for motor insurance to study the impact of experience rating in ruin probabilities. For that, we used a real commercial scale of an insurer operating in the Portuguese market, and we also work on various well-known optimal bonus-malus scales estimated with real data from that insurer. Results involving these scales are discussed.
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SASTRI, Ida I. Dewa Ayu Manik, Luh Kade DATRINI, and Ni Putu PERTAMAWATI. "The Role of Tax Incentives During the Covid-19 Pandemic Period and Stable Sustainable Economic Growth." International Journal of Environmental, Sustainability, and Social Science 2, no. 2 (July 30, 2021): 94–100. http://dx.doi.org/10.38142/ijesss.v2i2.79.
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The COVID-19 pandemic is a national disaster so the need for arrangements to support the handling of COVID-19 continues to be pursued. The real sector is expected to be able to survive and not terminate employment. The multiplier effect due to the covid pandemic requires government assistance as a policyholder. Taxes are a source of state finance, now changing to a second function, namely the regular function. Government Regulation No. 23, 44, 86, 110 and 143 regarding tax incentives for taxpayers affected by the coronavirus pandemic 19. Of the total 68,101 taxpayers at the Directorate General of Taxes in Bali, only 16,624 take advantage of tax incentives, so it must be investigated why taxpayers do not make optimal use of incentives that should be used to stimulate economic growth. The methodology used in this study is a descriptive interpretative qualitative method. The results of the study found that incentives used by taxpayers have stimulated economic growth, but there are taxpayers who do not take advantage of incentives due to the complexity of procedures and some do not receive information about incentives so that in the future the Directorate General of Taxes needs to simplify procedures and wider socialization.
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Lin, Jyh-Horng, Fu-Wei Huang, and Shi Chen. "Sunflower management and life insurance: modeling the CEO’s utility function." Review of Behavioral Finance 11, no. 3 (August 12, 2019): 309–23. http://dx.doi.org/10.1108/rbf-05-2018-0053.
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Purpose The purpose of this paper is to develop a theoretical framework to answer the following question: What are the consequences of sunflower behavior as well as spread behavior for how asset-liability management is administrated in a life insurance company? Design/methodology/approach This paper takes into account the following: the chief executive officer (CEO) of a life insurance company confirms the board of directors’ belief – the preference of the like of higher return relative to the dislike of higher risk; the authors call such behavior sunflower management; the life insurance policyholder is entitled to a guaranteed interest rate and a participation percentage of the company’s investment surplus; and the authors examine the optimal insurer interest margin, i.e., the spread between the loan rate and the guaranteed rate. Findings Sunflower management translates into lower utility for the CEO and makes the CEO more prudent to risk-taking at an increased insurer interest margin for the provision of life insurance contracts. The effect of the guaranteed rate on the margin is ambiguous and depends on the level of guarantee itself. An increase in the participation level decreases the CEO’s loan risk-taking at an increased margin. It is shown that a trend toward higher return like of the board’s belief produces a corresponding trend toward the CEO’s decreasing risk-taking when the return like is revealed strongly. The results indicate that sunflower management as such is an important determinant in ensuring a safe insurance system. Originality/value This is the first paper to construct a contingent claim model to evaluate the expected value of the CEO’s utility function defined in terms of the equity returns and the equity risks of a life insurance company. The model explicitly considers CEO sunflower behavior, CEO spread behavior and the limited liability of shareholders.
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Chen, An, Manuel Rach, and Thorsten Sehner. "ON THE OPTIMAL COMBINATION OF ANNUITIES AND TONTINES." ASTIN Bulletin 50, no. 1 (January 2020): 95–129. http://dx.doi.org/10.1017/asb.2019.37.
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AbstractTontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity, but provides a less volatile retirement income than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: the previously introduced “tonuity”, a product very similar to the tonuity which we call “antine” and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity and an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine. Further, we derive conditions on the premium loadings of annuities and tontines indicating when the optimal portfolio is investing a positive amount in both annuity and tontine, and when the optimal portfolio turns out to be a pure annuity or a pure tontine.
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Bernard, Carole, Fangda Liu, and Steven Vanduffel. "Optimal insurance in the presence of multiple policyholders." Journal of Economic Behavior & Organization 180 (December 2020): 638–56. http://dx.doi.org/10.1016/j.jebo.2020.02.012.
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Emms, Paul, and Steven Haberman. "Pricing General Insurance Using Optimal Control Theory." ASTIN Bulletin 35, no. 02 (November 2005): 427–53. http://dx.doi.org/10.2143/ast.35.2.2003461.
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Insurance premiums are calculated using optimal control theory by maximising the terminal wealth of an insurer under a demand law. If the insurer sets a low premium to generate exposure then profits are reduced, whereas a high premium leads to reduced demand. A continuous stochastic model is developed, which generalises the deterministic discrete model of Taylor (1986). An attractive simplification of this model is that existing policyholders should pay the premium rate currently set by the insurer. It is shown that this assumption leads to a bang-bang optimal premium strategy, which cannot be optimal for the insurer in realistic applications. The model is then modified by introducing an accrued premium rate representing the accumulated premium rates received from existing and new customers. Policyholders pay the premium rate in force at the start of their contract and pay this rate for the duration of the policy. It is shown that, for two demand functions, an optimal premium strategy is well-defined and smooth for certain parameter choices. It is shown for a linear demand function that these strategies yield the optimal dynamic premium if the market average premium is lognormally distributed.
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Emms, Paul, and Steven Haberman. "Pricing General Insurance Using Optimal Control Theory." ASTIN Bulletin 35, no. 2 (November 2005): 427–53. http://dx.doi.org/10.1017/s051503610001432x.
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Insurance premiums are calculated using optimal control theory by maximising the terminal wealth of an insurer under a demand law. If the insurer sets a low premium to generate exposure then profits are reduced, whereas a high premium leads to reduced demand. A continuous stochastic model is developed, which generalises the deterministic discrete model of Taylor (1986). An attractive simplification of this model is that existing policyholders should pay the premium rate currently set by the insurer. It is shown that this assumption leads to a bang-bang optimal premium strategy, which cannot be optimal for the insurer in realistic applications.The model is then modified by introducing an accrued premium rate representing the accumulated premium rates received from existing and new customers. Policyholders pay the premium rate in force at the start of their contract and pay this rate for the duration of the policy. It is shown that, for two demand functions, an optimal premium strategy is well-defined and smooth for certain parameter choices. It is shown for a linear demand function that these strategies yield the optimal dynamic premium if the market average premium is lognormally distributed.
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Müller, Katja, Hato Schmeiser, and Joël Wagner. "The impact of auditing strategies on insurers’ profitability." Journal of Risk Finance 17, no. 1 (January 18, 2016): 46–79. http://dx.doi.org/10.1108/jrf-05-2015-0045.
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Purpose – The purpose of this paper paper is to study effective measures in dealing with the phenomenon of insurance claims’ fraud. In fact, fraud is one of the major industry concerns. It occurs in all classes of insurance and accounts for a substantial portion of indemnity payments each year. Design/methodology/approach – This paper develops a model framework based on a costly state verification setting in which – while policyholders observe the amount of loss privately – the insurance company can decide to audit incoming claims at some cost. The aim is to derive optimal auditing strategies from the insurance company’s perspective while maintaining contract attractiveness to policyholders willing to adhere to the insurance relationship. The possibility for each stakeholder to adapt its behavioral strategy over the course of several periods is taken into account. Using a numerical approach based on Monte Carlo simulations, the impact of different parameterizations on the optimal auditing range by means of a sensitivity analysis is illustrated and analyzed. Findings – The central outcome of the model is an auditing range which selects those claims which should be subject to verification. Practical implications – This paper comes to the conclusion that, given some constant cost per audit, it is optimal to verify the accuracy of claims from the mid-value segment. Furthermore, it can be shown that while the option to adapt one’s strategy might be favorable from the insurance company perspective, it has a negative impact on the policyholders’ position. This disproves the common belief that adapting the defrauding strategy with the help of signals from service providers would be advantageous. Originality/value – This paper extends the stand of literature on costly state verification and gives indications for optimal auditing strategies in industry practice.
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Hofmann, Annette, Ole V. Häfen, and Martin Nell. "Optimal Insurance Policy Indemnity Schedules With Policyholders’ Limited Liability and Background Risk." Journal of Risk and Insurance 86, no. 4 (March 23, 2018): 973–88. http://dx.doi.org/10.1111/jori.12247.
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Jacob, Azaare, and Zhao Wu. "An Alternative Pricing System through Bayesian Estimates and Method of Moments in a Bonus-Malus Framework for the Ghanaian Auto Insurance Market." Journal of Risk and Financial Management 13, no. 7 (July 3, 2020): 143. http://dx.doi.org/10.3390/jrfm13070143.
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This paper examines the current No-Claim Discount (NCD) system used in Ghana’s auto insurance market as inefficient and outmoded and, therefore, proposes an alternative optimal Bonus-Malus System (BMS) intended to meet the present market conditions and demand. It appears that the existing BMS fails to acknowledge the frequency and severity of policyholders’ claims in its design. We minimized the auto insurance portfolios’ risk through Bayesian estimation and found that the risk is well fitted by gamma, with the claim distribution modeled by the negative binomial law with the expected number of claims (a priori) as 14%. The models presented in this paper recognize the longevity of accident-free driving and fully reward higher discounts to policyholders from the second year when the true characteristics of the hidden risks posed to the pool have been ascertained. The BMS finally constructed using the net premium principle is very optimal and has reasonable punishment and rewards for both good and bad drivers, which could also be useful in other developing economies.
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Sun, Jin, Pavel Shevchenko, and Man Fung. "The Impact of Management Fees on the Pricing of Variable Annuity Guarantees." Risks 6, no. 3 (September 19, 2018): 103. http://dx.doi.org/10.3390/risks6030103.
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Variable annuities, as a class of retirement income products, allow equity market exposure for a policyholder’s retirement fund with optional guarantees to limit the downside risk of the market. Management fees andguarantee insurance fees are charged respectively for the market exposure and for the protection from the downside risk. We investigate the pricing of variable annuity guarantees under optimal withdrawal strategies when management fees are present. We consider from both policyholder’s and insurer’s perspectives optimal withdrawal strategies and calculate the respective fair insurance fees. We reveal a discrepancy where the fees from the insurer’s perspective can be significantly higher due to the management fees serving as a form of market friction. Our results provide a possible explanation of lower guarantee insurance fees observed in the market than those predicted from the insurer’s perspective. Numerical experiments are conducted to illustrate the results.
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Bourgeon, Jean-Marc, and Pierre Picard. "Fraudulent Claims and Nitpicky Insurers." American Economic Review 104, no. 9 (September 1, 2014): 2900–2917. http://dx.doi.org/10.1257/aer.104.9.2900.
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Insurers have the reputation of being bad payers who nitpick whenever an opportunity arises. However, this nitpicking activity has a positive impact on their auditing strategy since auditing may prove profitable when claims are not fraudulent. We show that reducing the indemnity payments of audited claims induces a lower fraud rate at equilibrium and that some degree of nitpicking is socially optimal when insurance fraud is a concern. Its remains optimal even if it induces adverse effects on policyholders' moral standards. (JEL D86, G22, K12, K42)
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Khan, Hayat. "A Nontechnical Guide on Optimal Incentives for Islamic Insurance Operators." Journal of Risk and Financial Management 12, no. 3 (July 25, 2019): 127. http://dx.doi.org/10.3390/jrfm12030127.
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The takaful industry is searching for an optimal model for Islamic insurance operation, which has turned out to be a challenging task. This paper translates the abstract scientific knowledge accumulated in the optimal contracting literature into a simple, nontechnical, analytical framework to analyze alternative business models which could be used by regulators to align the best interest of shareholders and policyholders in the takaful industry. This paper shows that the wakalah–surplus-sharing hybrid serves as the optimal structure for takaful operation; in the presence of Akerlof’s (1982) gift-exchange, the wakalah fee reduces the adverse selection problem; and the wakalah fee could be used to protect infant takaful operators.
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Baione, Fabio, Susanna Levantesi, and Massimiliano Menzietti. "The Development of an Optimal Bonus-Malus System in a Competitive Market." ASTIN Bulletin 32, no. 1 (May 2002): 159–70. http://dx.doi.org/10.2143/ast.32.1.1021.
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AbstractBMS in force show a progressive reduction of the observed average premium, which causes a financial imbalance in the system (see Lemaire (1995)). As a onsequence, frequent premium adjustments become necessary and result in discrepancy between the reduction defined in the policy contract and the ffective discount applied to the driver. Most policyholders are not aware of his “lack of transparency”. This paper deals with the problem of designing an optimal tariff structure so that the designed BMS is adequate and satisfies both transparency and financial balance conditions.
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Zaks, Yaniv, Esther Frostig, and Benny Levikson. "Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level." ASTIN Bulletin 36, no. 01 (May 2006): 161–85. http://dx.doi.org/10.2143/ast.36.1.2014148.
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Consider a portfolio containing heterogeneous risks, where the policyholders’ premiums to the insurance company might not cover the claim payments. This risk has to be taken into consideration in the premium pricing. On the other hand, the premium that the insureds pay has to be fair. This fairness is measured by the distance between the risk and the premium paid. We apply a non-linear programming formulation to find the optimal premium for each class so that the risk is below a given level and the weighted distance between the risk and the premium is minimized. We consider also the dual problem: minimizing the risk level for a given weighted distance between risks and premium.
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Zaks, Yaniv, Esther Frostig, and Benny Levikson. "Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level." ASTIN Bulletin 36, no. 1 (May 2006): 161–85. http://dx.doi.org/10.1017/s0515036100014446.
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Consider a portfolio containing heterogeneous risks, where the policyholders’ premiums to the insurance company might not cover the claim payments. This risk has to be taken into consideration in the premium pricing. On the other hand, the premium that the insureds pay has to be fair. This fairness is measured by the distance between the risk and the premium paid. We apply a non-linear programming formulation to find the optimal premium for each class so that the risk is below a given level and the weighted distance between the risk and the premium is minimized. We consider also the dual problem: minimizing the risk level for a given weighted distance between risks and premium.
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Guerreiro, Gracinda Rita, João Tiago Mexia, and Maria de Fátima Miguens. "STATISTICAL APPROACH FOR OPEN BONUS MALUS." ASTIN Bulletin 44, no. 1 (October 18, 2013): 63–83. http://dx.doi.org/10.1017/asb.2013.26.
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AbstractIn this paper, following an open portfolio approach, we show how to estimate a Bonus-malus system evolution.Considering a model for the number of new annual policies, we obtain ML estimators, asymptotic distributions and confidence regions for the expected number of new policies entering the portfolio in each year, as well as for the expected number and proportion of insureds in each bonus class, by year of enrollment. Confidence regions for the distribution of policyholders result in confidence regions for optimal bonus scales.Our treatment is illustrated by an example with numerical results.
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Goffard, Pierre-Olivier, and Xavier Guerrault. "Is it optimal to group policyholders by age, gender, and seniority for BEL computations based on model points?" European Actuarial Journal 5, no. 1 (April 17, 2015): 165–80. http://dx.doi.org/10.1007/s13385-015-0106-7.
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Engsner, Hampus, Kristoffer Lindensjö, and Filip Lindskog. "The value of a liability cash flow in discrete time subject to capital requirements." Finance and Stochastics 24, no. 1 (September 27, 2019): 125–67. http://dx.doi.org/10.1007/s00780-019-00408-0.
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Abstract The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the presented approach is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity, whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner’s perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.
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Boyer, M. M., and C. M. Nyce. "Insuring catastrophes and the role of governments." Natural Hazards and Earth System Sciences 13, no. 8 (August 16, 2013): 2053–63. http://dx.doi.org/10.5194/nhess-13-2053-2013.
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Abstract. In this paper we model the cost of providing insurance coverage against natural and man-made hazards. We propose an insurance market model that explains (1) the use of reinsurance to help finance the cost of catastrophic events and (2) the implicit (or explicit) presence of government entities acting as (re)insurers of last resort. Using an economic model, we show how insurance programmes should be designed to cover the losses due to a possible catastrophic natural hazard. Our results show that the optimal structure of a reinsurance programme minimizes the cost of offering insurance protection. We also show how government intervention can reduce the cost of insurance against natural catastrophes and increase policyholders' welfare. Our paper therefore offers public policy implications as to the role and presence of government as an insurer of last resort and the minimum insurance premium necessary to cover the cost of catastrophic events.
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SERRANO, RAFAEL. "PORTFOLIO ALLOCATION IN A LEVY-TYPE JUMP-DIFFUSION MODEL WITH NONLIFE INSURANCE RISK." International Journal of Theoretical and Applied Finance 24, no. 01 (February 2021): 2150005. http://dx.doi.org/10.1142/s0219024921500059.
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We propose a model that integrates investment, underwriting, and consumption/dividend policy decisions for a nonlife insurer by using a risk control variable related to the wealth-income ratio of the firm. This facilitates the efficient transfer of insurance risk to capital markets since it allows to select simultaneously investments and underwriting volume. The model is particularly valuable for business lines with significant exposure to extreme events and disaster risk, as it accounts for features usually depicted during negative economic shocks and catastrophic events, such as Levy-type jump-diffusion dynamics for the financial log-returns that are in turn correlated with insurance premiums and liabilities, as well as worst-case scenarios in which policyholders in the insurance portfolio report claims with the same severity simultaneously. Using the martingale method, we determine an optimal solvency threshold or wealth-income ratio, and investment strategy that maximizes the expected utility from dividend payouts that follows a (possibly stochastic) consumption clock. We illustrate the main results with numerical examples for log- and power-utility functions, and (bounded variation) tempered stable Levy jumps.
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Loisel, Stéphane, Pierrick Piette, and Cheng-Hsien Jason Tsai. "APPLYING ECONOMIC MEASURES TO LAPSE RISK MANAGEMENT WITH MACHINE LEARNING APPROACHES." ASTIN Bulletin 51, no. 3 (June 4, 2021): 839–71. http://dx.doi.org/10.1017/asb.2021.10.
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AbstractModeling policyholders’ lapse behaviors is important to a life insurer, since lapses affect pricing, reserving, profitability, liquidity, risk management, and the solvency of the insurer. In this paper, we apply two machine learning methods to lapse modeling. Then, we evaluate the performance of these two methods along with two popular statistical methods by means of statistical accuracy and profitability measure. Moreover, we adopt an innovative point of view on the lapse prediction problem that comes from churn management. We transform the classification problem into a regression question and then perform optimization, which is new to lapse risk management. We apply the aforementioned four methods to a large real-world insurance dataset. The results show that Extreme Gradient Boosting (XGBoost) and support vector machine outperform logistic regression (LR) and classification and regression tree with respect to statistic accuracy, while LR performs as well as XGBoost in terms of retention gains. This highlights the importance of a proper validation metric when comparing different methods. The optimization after the transformation brings out significant and consistent increases in economic gains. Therefore, the insurer should conduct optimization on its economic objective to achieve optimal lapse management.
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Yin, Shuang, Guojun Gan, Emiliano A. Valdez, and Jeyaraj Vadiveloo. "Applications of Clustering with Mixed Type Data in Life Insurance." Risks 9, no. 3 (March 3, 2021): 47. http://dx.doi.org/10.3390/risks9030047.
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Death benefits are generally the largest cash flow items that affect the financial statements of life insurers; some may still not have a systematic process to track and monitor death claims. In this article, we explore data clustering to examine and understand how actual death claims differ from what is expected—an early stage of developing a monitoring system crucial for risk management. We extended the k-prototype clustering algorithm to draw inferences from a life insurance dataset using only the insured’s characteristics and policy information without regard to known mortality. This clustering has the feature of efficiently handling categorical, numerical, and spatial attributes. Using gap statistics, the optimal clusters obtained from the algorithm are then used to compare actual to expected death claims experience of the life insurance portfolio. Our empirical data contained observations of approximately 1.14 million policies with a total insured amount of over 650 billion dollars. For this portfolio, the algorithm produced three natural clusters, with each cluster having lower actual to expected death claims but with differing variability. The analytical results provide management a process to identify policyholders’ attributes that dominate significant mortality deviations, and thereby enhance decision making for taking necessary actions.
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Rao T, VSRNR, Sakshi Dua, and Priya Saha. "Identifying Black Rice Cultivated Area Using Sentinel2." Journal of Scientific Research 66, no. 02 (2022): 214–19. http://dx.doi.org/10.37398/jsr.2022.660228.
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Kalabati(Oriza Sativia L.) is a black or forbidden rice variety with rich medicinal and nutrient values. Traditionally, several studies acknowledged the unlimited potential of black rice and intensive research conducted in the laboratory environment to determine its benefits. The presence of anthocyanin(anth) content in Kalbati rice plants turns leaves into black or purple. Several studies identified rice canopy using remote sensing technologies, but none attempted to distinguish black rice areas. Understanding the existence and yield of black rice helps governments or policyholders to take appropriate decisions to promote its benefits in society for broader consumption. This study aims to evaluate the feasibility of using satellite imagery to identify the anth content of Kalabati plant leaves using leaf optical properties. Sentinel2 based indices help to identify Anth content in the leaves using its multi-spectral(MSI) instrument. A combination of Modified Anthocyanin Index(mARI), Chlorophyll Vegetation Index(CVI) and Green Leaf Index(GLI) is used to determine the complex rice canopy of the black rice that exists at a negligible percentage among other crops. The correlation of mARI with CVI has an RMSE value of 0.11314, and the same RMSE value of mARI with GLI is at 0.66441. Finally, the study concluded anth content in Kalabati rice could be interpreted using multi-spectral data from Sentinel-2.c
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Wahono, Tri, Endang Puji Astuti, Andri Ruliansyah, Mara Ipa, and Muhammad Umar Riandi. "Studi Kualitatif Implementasi Kebijakan Eliminasi Malaria di Wilayah Endemis Rendah Kabupaten Pangandaran dan Pandeglang." ASPIRATOR - Journal of Vector-borne Disease Studies 13, no. 1 (June 29, 2021): 55–68. http://dx.doi.org/10.22435/asp.v13i1.4683.
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The government targets malaria elimination in Java and Bali by 2023. But until 2020, Pangandaran and Pandeglang Regency haven’t received malaria-free certification. This qualitative study was conducted to provide an overview of Pangandaran and Pandeglang malaria control implementation by comparing it to Activity Indicators based on the Indonesian Minister of Health Decree on malaria elimination. In-depth interviews, using thematically interview guidelines, were conducted to 48 key informants such as policyholders and people in charge of health programs and cross-sectoral at the provincial, district, sub-district, and village levels. Thematic analysis was used in the theme of policy implementation, budget, facilities and infrastructures, human resources, and cross-sector cooperation. The result shows that malaria control is implemented according to the decree, but some activities haven’t been done. The analysis on policy implementation theme shows that both districts have carried out according to the guidelines, with innovation in the form of establishing Posmaldes (village malaria post) in Ujung Kulon National Park in Pandeglang. APBD, APBN, and Global Fund are used as budget sources. Both districts stated that facilities and infrastructures are sufficiently available, but there is a lack in human resources’ quantity and varying degrees of competencies. There is also a lack of cross-sector cooperation because malaria control hasn’t become a priority in those sectors and they are only acting as supports to the health sector. Efforts to control malaria are considered less optimal due to the absence of malaria elimination regulations, varied human resource capabilities, and the limitation in the duties and functions of cross-sectors.
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Tkachenko, K., and I. Paska. "Methodical approaches to optimizing the insurance company portfolio of services." Ekonomìka ta upravlìnnâ APK, no. 2 (169) (December 9, 2021): 164–72. http://dx.doi.org/10.33245/2310-9262-2021-169-2-164-172.
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The article is devoted to the generalization of methodological approaches to the optimization of the insurance company portfolio of services and the development of an algorithm for optimizing the insurance company's services portfolio. Insurance market of Ukraine is in a state of transformation, which is associated with changes in the institutional conditions of insurance, changes in the priorities of policyholders, macroeconomic instability, the spread of the COVID-19 pandemic. Institutional changes in the insurance market of Ukraine and macroeconomic instability have led to the "cleansing" of the insurance market and the exit of insurance companies that do not ensure transparency, solvency and efficiency. In the three quarters of 2021, 41 insurance companies left the Ukrainian insurance market, ie one in five insurance companies ceased operations. The relevance of optimizing the insurance company's portfolio of services is proved, which is due to the need for insurance companies to review their own portfolios to ensure financial stability, solvency and efficiency in a competitive insurance market of Ukraine. It is proposed to consider the optimization of the insurance company's portfolio of services as a set of interconnected and consecutive stages that are consistent and logical, as well as adaptive to modern realities of the insurance market of Ukraine, aimed at achieving profitability and maximizing the value of the insurance company. The first five stages of optimizing the insurance company's portfolio should be considered the most important, as it provides for determining the methodological principles of optimizing the insurance portfolio. Substantiation of the type of insurance company's portfolio and justification of the list of criteria for optimizing the insurance company's portfolio are interrelated stages that determine the individual basic parameters of the optimized portfolio for the insurance company depending on the chosen type of portfolio. Calculations for the optimization of the insurance company's portfolio of services involve the implementation of economic and mathematical modeling of the structure of the insurance services portfolio and the definition of its targets. Following a certain period of time, the insurance company must assess the effectiveness of achieving the optimal portfolio of services of the insurance company and the impact on key performance indicators of the insurance company, including net financial result and value of the insurance company, the presence of deviations of actual and optimal indicators. Keywords: insurance, insurance company, insurance company portfolio, optimization, Markovic model, insurance market of Ukraine.
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Petrenko, Olga. "Institutional Support of Agricultural Market Development." Modern Economics 28, no. 1 (August 20, 2021): 113–18. http://dx.doi.org/10.31521/modecon.v28(2021)-16.
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Abstract.Introduction. The article considers the problem of institutional support for the development of the agricultural insurance market in Ukraine. The substantiation of the algorithm of reproduction of dynamic process of institutional development which is offered to be realized in three stages is given: 1) assistance of growth of mutual trust of operating subjects of the agroinsurance market; 2) settlement of consolidated liability of all participants in the insurance process in the agricultural sector; 3) creation of conditions for the functioning of a proper insurance environment in the agricultural insurance market. Results. Strategic directions of improving the institutional environment of the agricultural insurance market on the basis of systematic coordination of relevant formal (various laws and regulations, insurance conditions, etc.) and informal institutions (insurance culture, moral and ethical values, etc.), effective infrastructure and information support, effective transaction cost management are proposed. domestic insurance companies, synergistic interaction of direct (insurers, insurers and intermediaries) and indirect (governmental and non-governmental institutions) participants in the agricultural insurance process. The key condition for optimal interaction of agricultural insurance market participants is to increase the level of development of its institutional support, focused on the distribution or redistribution of risks and liability in the time lag. Conclusions.Thus, the process of institutional support for the development of the agricultural insurance market should be considered in terms of algorithmic settlement of insurance interests and opportunities for integration of formal, informal, functional and structural institutions, which are focused on ensuring a culture of providing and consuming agricultural insurance services. Emphasis is placed on the fact that the institutional support for the development of the agricultural insurance market is based on the formation of stable effective demand of potential policyholders for certain insurance services and their direct generation by various insurance companies to timely cover emerging agricultural insurance risks. To promote the sustainability of the agricultural insurance market is its modernization, which focuses on the systematic adoption of strategic measures to organize the reproduction of a proper favorable insurance environment in agricultural insurance.
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Jeon, Junkee, and Minsuk Kwak. "A variational inequality arising from optimal surrender of variable annuity with lookback benefit." Journal of Inequalities and Applications 2022, no. 1 (January 4, 2022). http://dx.doi.org/10.1186/s13660-021-02743-3.
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AbstractWe introduce a variable annuity (VA) contract with a surrender option and lookback benefit, that is, the benefit of the VA contract is linked to the maximum process of the policyholder’s account value. In contrast to the constant guarantee model provided in Bernard et al. (Insur. Math. Econ. 55:116–128, 2014), it is optimal for the policyholder of the VA contract with lookback benefit to surrender the VA contract when the policyholder’s account value is below or equal to the optimal surrender boundary. Thus, from the perspective of the insurer to construct a portfolio of VA contracts, utilizing the VA contracts with lookback benefit along with VA contracts with constant guarantee provides the diversification of early surrenders. The valuation of this contract can be described as a two-dimensional parabolic variational inequality. By converting this into the one-dimensional problem, we obtain the integral equations for the value function and the free boundary. The recursive integration method is applied to obtain the numerical solutions. We also provide comparative statics of the optimal surrender boundaries with respect to various parameters.
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Payandeh Najafabadi, Amir T., and Saeed MohammadPour. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems." Asia-Pacific Journal of Risk and Insurance 12, no. 2 (April 7, 2018). http://dx.doi.org/10.1515/apjri-2017-0014.
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Abstract This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model’s parameters. Then, such new model along with a Pareto mixture model have employed to design an optimal rate–making system. Namely, this article employs number/size of reported claims of Iranian third party insurance dataset. Then, it employs the k-Inflated Negative Binomial mixture distribution/regression model as well as other well developed counting models along with a Pareto mixture model to model frequency/severity of reported claims in Iranian third party insurance dataset. Such numerical illustration shows that: (1) the k-Inflated Negative Binomial mixture models provide more fair rate/pure premiums for policyholders under a rate–making system; and (2) in the situation that number of reported claims uniformly distributed in past experience of a policyholder (for instance $k_1=1$ and $k_2=1$ instead of $k_1=0$ and $k_2=2$). The rate/pure premium under the k-Inflated Negative Binomial mixture models are more appealing and acceptable.
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Moenig, Thorsten, and Daniel Bauer. "Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities." SSRN Electronic Journal, 2021. http://dx.doi.org/10.2139/ssrn.3797995.
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Qu, Shaojian, Shan Jiang, and Can Feng. "A new robust insurance model considering the time of accident." Journal of Intelligent & Fuzzy Systems, June 3, 2022, 1–20. http://dx.doi.org/10.3233/jifs-212391.
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The principle of maximum utility is generally adopted to design the optimal insurance contracts, which should consider the influence of different factors such as the probability of accident, premium, compensation, and so on. However, most literatures deal with these variables from a static perspective. This paper considers the accident probability and the value of insurance subject based on the time of accident, which is rarely involved in the previous studies and considers the utility function of the insurer and the policyholder from a dynamic perspective. Firstly, to make this model more universally applicable, we establish an insurance model that considers the time of the accident and different premium payment forms for policy-holders and insurers respectively. Next, we derive a robust premium insurance model based on min-max regret, in which the time of the accident can be assumed to be certain and uncertain respectively. Then, we conduct numerical experiments and analyze the utility of the policy-holders, demonstrating guarantee period and value of insurance subject are significant when insuring and derive the optimal coverage rate. These results also show that the insurance model that takes into account the time of accident performs better.
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Bernard, Carole, Fangda Liu, and Steven Vanduffel. "Impact of Preferences on Optimal Insurance in the Presence of Multiple Policyholders." SSRN Electronic Journal, 2018. http://dx.doi.org/10.2139/ssrn.3270247.
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