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1
Khalil, Elias L. "Chaos Theory Versus Heisenberg's Uncertainty: Risk, Uncertainty and Economic Theory." American Economist 41, no. 2 (October 1997): 27–40. http://dx.doi.org/10.1177/056943459704100204.
Повний текст джерелаАнотація:
The paper argues that there is a fundamental difference between the indeterminism of chaos theory and the indeterminism of quantum mechanics. The difference somewhat resembles Knight's distinction between risk and uncertainly. Theorists interested in going beyond equilibrium economics have failed to notice the difference. Therefore, they confuse between two kinds of economic change which involve indeterminism, viz., nonlinear dynamics and technological/institutional development. They also regard the evolutionary paradigm as an alternative of the equilibrium one—whereas each deals with a different phenomenon.
2
Thomas, Robert, Marilyn Eichelberger, and Missey Lee. "The Theory of Risk Uncertainty Reduction." Journal of System Safety 54, no. 2 (October 1, 2018): 11–18. http://dx.doi.org/10.56094/jss.v54i2.73.
Повний текст джерелаАнотація:
The objective of this research is to examine the character of safety programs in not only reducing risk, but also in reducing relative risk uncertainty. This paper approximates the distributions of both the probability and severity of a mishap as lognormal and examines the likely behavior of the co-distribution as the safety process is executed. This paper also shows how differential forces across the risk plane reduce both the risk itself and the relative uncertainty in the risk at the same time. With this new approach, risk now becomes a quantitative item with a known probability distribution, providing a new metric for safety program effectiveness.
3
Bélyácz, Iván, and Katalin Daubner. "Uncertainity of risk and increasing risk of uncertainty in business decisions." Economy & finance 8, no. 3 (2021): 264–312. http://dx.doi.org/10.33908/ef.2021.3.2.
Повний текст джерелаАнотація:
Our paper follows the development of theory regarding the position of risk and uncertainty in economics from the publication of works by Knight (1921) and Keynes (1921) until the recent past. The starting point is presented by the relevant remarks of the thinkers of classical economics. Next, we describe the turning point related to Knight and Keynes and reveal the theoretical roots of risk taking. In the core chapter of the paper the authors make an attempt to re-interpret “animal spirits” as the intention for risk taking. A separate chapter is devoted to the relationship of rational choice and risk, and another one about the canonisation of risk in economics. In further parts of the paper, we examine the intentions to relativize the difference between risk and uncertainty, the negligence of uncertainty in the neo-classical system, the attempts to merge risk and uncertainty and the disruption of the unity of risk taking and risk bearing. Finally, the authors come to the conclusion that Knight’s and Keynes’ doctrines of risk and uncertainty have stood the test of time.
4
Huang, Hong, and Yufu Ning. "Risk-Neutral Pricing Method of Options Based on Uncertainty Theory." Symmetry 13, no. 12 (December 1, 2021): 2285. http://dx.doi.org/10.3390/sym13122285.
Повний текст джерелаАнотація:
In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options.
5
He, Zhiguo, Si Li, Bin Wei, and Jianfeng Yu. "Uncertainty, Risk, and Incentives : Theory and Evidence." Finance and Economics Discussion Series 2013, no. 18 (February 2013): 1–37. http://dx.doi.org/10.17016/feds.2013.18.
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He, Zhiguo, Si Li, Bin Wei, and Jianfeng Yu. "Uncertainty, Risk, and Incentives: Theory and Evidence." Management Science 60, no. 1 (January 2014): 206–26. http://dx.doi.org/10.1287/mnsc.2013.1744.
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7
Vercelli, Alessandro. "From Soft Uncertainty to Hard Environmental Uncertainty." Économie appliquée 48, no. 2 (1995): 251–69. http://dx.doi.org/10.3406/ecoap.1995.1565.
Повний текст джерелаАнотація:
The distinction between different modalities of uncertainty is crucial for the analysis of environmental risk associated with economic activity. The distinction here introduced between soft uncertainty and hard uncertainty is based on recent advances in probability theory and decision theory under uncertainty. Environmental risk associated with economic development often occurs under hard uncertainty and irreversibility and can be controlled only through a wise use of preventive policy instruments able to eliminate or mitigate it.
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Lio, Waichon, and Lifen Jia. "Uncertain production risk process with breakdowns and its shortage index and shortage time." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 7151–60. http://dx.doi.org/10.3233/jifs-200453.
Повний текст джерелаАнотація:
Since the practical production is not continuously available and sometimes suffers unexpected breakdowns, this paper applies uncertainty theory to introducing an uncertain production risk process with breakdowns to handle the production problem with uncertain cycle times (consisting of uncertain on-times and uncertain off-times) and uncertain production amounts. The concept of shortage index of the uncertain production risk process with breakdowns is provided and some formulas for the calculation are given. Furthermore, the shortage time of the uncertain production risk process with breakdowns is proposed and its uncertainty distribution is obtained. Finally, some numerical examples are revealed.
9
Beranová, M., and D. Martinovičová. "Application of the theory of decision making under risk and uncertainty at modelling of costs." Agricultural Economics (Zemědělská ekonomika) 56, No. 5 (June 1, 2010): 201–8. http://dx.doi.org/10.17221/88/2009-agricecon.
Повний текст джерелаАнотація:
The costs functions are mentioned mostly in the relation to the Break-even Analysis where they are presented in the linear form. But there exist several different types and forms of cost functions. Fist of all, it is necessary to distinguish between the short-run and long-run cost function that are both very important tools of the managerial decision making even if each one is used on a different level of management. Also several methods of estimation of the cost function's parameters are elaborated in the literature. But all these methods are based on the past data taken from the financial accounting while the financial accounting is not able to separate the fixed and variable costs and it is also strongly adjusted to taxation in the many companies. As a tool of the managerial decision making support, the cost functions should provide a vision to the future where many factors of risk and uncertainty influence economic results. Consequently, these random factors should be considered in the construction of cost functions, especially in the long-run. In order to quantify the influences of these risks and uncertainties, the authors submit the application of the Bayesian Theorem.
10
Shao, Wei. "Economic Policy Uncertainty and Corporate Innovation Behavior." Frontiers in Sustainable Development 4, no. 8 (August 21, 2024): 6–11. http://dx.doi.org/10.54691/va1cem84.
Повний текст джерелаАнотація:
This paper explores the impact of economic policy uncertainty on corporate innovation behavior. By integrating uncertainty theory, innovation theory, and real options theory, it constructs a comprehensive theoretical framework to explain how economic policy uncertainty affects corporate innovation decisions. Specifically, the paper posits that economic policy uncertainty influences corporate risk assessment, investment decisions, and option realization, ultimately having a profound impact on their innovation activities. This paper analyzes in detail the strategies that companies might adopt when facing economic policy uncertainty, including delaying investments, phased innovation investments, and diversified innovation investments. These strategies aim to minimize the risks brought about by policy uncertainty while maintaining the company's competitiveness and innovative capabilities in the market. Additionally, this paper proposes a series of hypotheses to further verify the specific impact of increased economic policy uncertainty on corporate innovation behavior. These hypotheses include: when economic policy uncertainty increases, companies will delay innovation investments; and in highly uncertain policy environments, companies tend to adopt diversified innovation investment strategies to spread risk. Finally, this paper provides valuable references from both corporate and governmental perspectives, helping corporate managers and policymakers formulate more effective innovation and management strategies in the context of economic policy uncertainty.
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Liu, Ying, Liuying Ma, Luyang Sun, Xiao Zhang, Yunyun Yang, Qing Zhao, and Zhigang Qu. "Risk-Based Maintenance Optimization for a Subsea Production System with Epistemic Uncertainty." Symmetry 14, no. 8 (August 11, 2022): 1672. http://dx.doi.org/10.3390/sym14081672.
Повний текст джерелаАнотація:
The lack of operation and maintenance data brings difficulties to traditional risk assessment based on probability methods. Therefore, experts are invited to evaluate the key performance indicators related to system risk. These evaluation results are usually described by ambiguous language, so they have epistemic uncertainty. Uncertainty theory is a branch of mathematics used to model experts’ degrees of belief. The uncertain measure has duality, that is, some symmetry, which means that the sum of the uncertain measure of an event and the uncertain measure of its complementary set is equal to 1. Therefore, the risk occurrence time of each basic event evaluated by experts is modeled by the uncertain variable in this article. Then, the risk assessment method of systems with epistemic uncertainty is proposed based on an uncertain fault tree analysis. Furthermore, two risk-based maintenance optimization models for systems with epistemic uncertainty are established. In particular, the leakage risk assessment method and the two risk-based maintenance optimization models for a subsea production system are considered, and the optimization results are given. The optimization results can help practitioners to warn of the leakage risk and make scientific maintenance decisions based on expert knowledge, so as to extend the service life of subsea production systems.
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Washington, Anne L. "Uncertain risk: assessing open data signals." Transforming Government: People, Process and Policy 14, no. 4 (June 17, 2020): 623–37. http://dx.doi.org/10.1108/tg-09-2019-0086.
Повний текст джерелаАнотація:
Purpose Open data resources contain few signals for assessing their suitability for data analytics. The purpose of this paper is to characterize the uncertainty experienced by open data consumers with a framework based on economic theory. Design/methodology/approach Drawing on information asymmetry theory about market exchanges, this paper investigates the practical challenges faced by data consumers seeking to reuse open data. An inductive qualitative analysis of over 2,900 questions asked between 2013 and 2018 on an internet forum identified how a community of 15,000 open data consumers expressed uncertainty about data sources. Findings Open data consumers asked direct questions that expressed uncertainty about the availability, interoperability and interpretation of data resources. Questions focused on future value and some requests were devoted to seeking data that matched known sources. The study proposes a data signal framework that explains uncertainty about open data within the context of control and visibility. Originality/value The proposed framework bridges digital government practice to information signaling theory. The empirical evidence substantiates market aspects of open data portals. This paper provided a needed case study of how data consumers experience uncertainty. The study integrates established theories about risk to improve the reuse of open data.
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Chen, Lijia, and Yanfei Tian. "Risk Cloud Model for Evaluating Nautical Navigational Environments." Mathematical Problems in Engineering 2021 (April 1, 2021): 1–15. http://dx.doi.org/10.1155/2021/8888865.
Повний текст джерелаАнотація:
Uncertainty makes the risk evaluation of complex water transportation systems (WTSs) a difficult task. To achieve reasonable results while accounting for uncertainty, the risk evaluation of nautical navigational environments (NNEts) is often based on classical cloud model theory. This study proposes the concept of a risk cloud model (RCM) for NNEt evaluation and uses a fuzzy statistics-based computational approach to obtain the RCM parameters. As a case study, the proposed RCM method was applied to the risk evaluation of the Qiongzhou Strait. The performance of the proposed method was compared to those of a fuzzy theory-based method and an earlier proposed simplified algorithm. The results of the case study demonstrated the effectiveness of the proposed method along with several key advantages. First, the method could deal with uncertainty, take advantage of multichannel information, and evaluate risk features. Second, the RCM droplets intuitively displayed the qualitative and quantitative characteristics of risk levels, which facilitated understanding and analysis. Third, it showed a good sensitivity to ensure the refinement of evaluation results. The proposed method offered an improved approach to NNEt risk evaluation under uncertain conditions.
14
NUSRAT, ELHUM, and KOICHI YAMADA. "A DESCRIPTIVE DECISION-MAKING MODEL UNDER UNCERTAINTY: COMBINATION OF DEMPSTER-SHAFER THEORY AND PROSPECT THEORY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, no. 01 (February 2013): 79–102. http://dx.doi.org/10.1142/s0218488513500050.
Повний текст джерелаАнотація:
In this paper, a descriptive decision-making model under uncertainty is proposed which incorporates two types of decision attitudes for uncertainty; one is an attitude about ignorance (optimism/pessimism) and the other one is about risk (risk-seeking and risk-aversion). At first, Evidential Decision Making Problem (EDMP) has been defined where Dempster-Shafer Theory (DST) has been used to represent uncertainty. Then probability approximation approach of solving EDMP is shown. For deciding the decision weights in different attitudes of decision maker, Ordered Weighted Averaging (OWA) operator has been used. Later on, Prospect Theory has been applied to accomplish a descriptive decision-making model. To show the effectiveness of our approach, a real life decision problem of travelers' route choice from a set of alternatives has also been provided.
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Ashtiani, Mehrdad, Shima Hakimi-Rad, and Mohammad Abdollahi Azgomi. "A Model of Trust Based on Uncertainty Theory." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 02 (April 2018): 269–98. http://dx.doi.org/10.1142/s0218488518500150.
Повний текст джерелаАнотація:
In trust management systems, the trustor should be able to select a trustee candidate that has the maximum trustworthiness degree toward a specific goal and an amount of risk consistent with her/his risk acceptance degree. In this research, a novel computational trust model based on the principles of uncertainty theory is introduced. In the proposed model, trust is considered to be constructed of trustworthiness components. To calculate each of these trustworthiness components, empirical distributions of recommenders and trustor’s opinions about the existing trustworthiness and risk degrees of the trustee candidates are aggregated. In the decision making stage, the trustee candidate with the optimum trustworthiness and risk degrees is selected according to uncertain goal programming. Based on this method, trustworthiness and risk degrees of the trustee candidates are calculated according to the amount of negative and positive deviations from the optimal state. To verify the accuracy of the model’s behavior, a series of simulation scenarios are constructed. The results of these simulations demonstrate that the proposed model effectively selects the best trustee candidate according to parameters such as context, priorities of the trustworthiness components, trustor’s constraints and the trustworthiness and risk acceptance degrees. Finally, by comparing the model with other commonly used computational trust modeling approaches, it is shown that the proposed model has a lower mean absolute error (MAE) and produces more accurate results.
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Zhou, Shuang, Jianguo Zhang, Lingfei You, and Qingyuan Zhang. "Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties." Eksploatacja i Niezawodnosc - Maintenance and Reliability 23, no. 2 (February 4, 2021): 231–41. http://dx.doi.org/10.17531/ein.2021.2.3.
Повний текст джерелаАнотація:
Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly, a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.
17
Wu, Lei, Yongchuan Tang, Liuyuan Zhang, and Yubo Huang. "Uncertainty Management in Assessment of FMEA Expert Based on Negation Information and Belief Entropy." Entropy 25, no. 5 (May 15, 2023): 800. http://dx.doi.org/10.3390/e25050800.
Повний текст джерелаАнотація:
The failure mode and effects analysis (FMEA) is a commonly adopted approach in engineering failure analysis, wherein the risk priority number (RPN) is utilized to rank failure modes. However, assessments made by FMEA experts are full of uncertainty. To deal with this issue, we propose a new uncertainty management approach for the assessments given by experts based on negation information and belief entropy in the Dempster–Shafer evidence theory framework. First, the assessments of FMEA experts are modeled as basic probability assignments (BPA) in evidence theory. Next, the negation of BPA is calculated to extract more valuable information from a new perspective of uncertain information. Then, by utilizing the belief entropy, the degree of uncertainty of the negation information is measured to represent the uncertainty of different risk factors in the RPN. Finally, the new RPN value of each failure mode is calculated for the ranking of each FMEA item in risk analysis. The rationality and effectiveness of the proposed method is verified through its application in a risk analysis conducted for an aircraft turbine rotor blade.
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Backus, G. B. C., V. R. Eidman, and A. A. Dijkhuizen. "Farm decision making under risk and uncertainty." Netherlands Journal of Agricultural Science 45, no. 2 (July 1, 1997): 307–28. http://dx.doi.org/10.18174/njas.v45i2.520.
Повний текст джерелаАнотація:
Relevant portions of the risk literature are reviewed, relating them to observed behaviour in farm decision-making. Relevant topics for applied agricultural risk research are proposed. The concept of decision making under risk and uncertainty is discussed by reviewing the theory of Subjective Expected Utility and its limitations. Subjective Expected Utility theory is the major framework for thinking systematically through complex issues of decision. Limitations of Subjective Expected Utility theory were that its application to unique decisions is doubtful, that it does not contribute to difficulties in determining the available decision alternatives, and that it is cast in a timeless setting, making the theoretic framework to a very limited extent helpful to solve real world decision problems. Most empirical studies indicate that farmers are risk neutral to slightly risk averse. It is doubtful whether decision makers could be classified according to their risk preferences. A presented overview of applied risk responses reveals much attention for diversification of the enterprise and of production practices, maintaining reserves, and farm expansion. Research reports on observed problems in farm decision making behaviour are lacking. Proposed topics for agricultural risk research include the assessment of the need for a strategic change, the creation of databases to determine both the (co)variances of input and output prices, the effectiveness of various kinds of decision support for different decision problems, and methods for applied scenario analysis to deal with long-run risk.
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Saldanha, Terence, Mariana Andrade-Rojas, Abhishek Kathuria, Jiban Khuntia, and Mayuram Krishnan. "How the Locus of Uncertainty Shapes the Influence of CEO Long-term Compensation on Information Technology Capital Investments." MIS Quarterly 48, no. 2 (June 1, 2024): 459–90. http://dx.doi.org/10.25300/misq/2023/17433.
Повний текст джерелаАнотація:
Firms must allocate resources effectively to cope with uncertainty, which can manifest as a disruption and an opportunity. Although information technology (IT) is a means to cope with uncertainty, chief executive officers (CEOs) may not always support IT investments due to the risky nature of IT, especially when facing uncertain conditions. While prior research suggests that CEO long-term compensation positively incentivizes IT investments, little is known about how different loci of uncertainty impact this relationship. To address this research gap, we study how firm-specific uncertainty and competitive uncertainty shape the influence of CEO long-term compensation on a firm’s IT capital investment. Drawing on agency theory and prospect theory, we develop two hypotheses. First, we hypothesize that firm-specific uncertainty and competitive uncertainty positively moderate the influence of CEO long-term compensation on firm IT capital investment. Second, we hypothesize that competitive uncertainty has a stronger positive moderating effect than firm-specific uncertainty on the influence of CEO long-term compensation on firm IT capital investment. Our analysis of secondary longitudinal data from 2000 to 2007 of 357 public firms in the United States supports our hypotheses. In exploratory analyses, we found that CEO long-term compensation results in a higher risk-oriented dominant logic in the firm, particularly in conditions of firm-specific uncertainty and competitive uncertainty, with competitive uncertainty having a stronger positive moderating effect. These findings uncover risk-oriented dominant logic as a theoretical mechanism that explains how CEO long-term compensation positively influences firm IT capital investment in uncertain conditions. We also conducted exploratory analyses using a different secondary dataset of 286 U.S. public firms from 2004 to 2019 to consider firm investments in transformative IT applications and found support for our theory. This finding triangulates our results across different time periods and different types of IT investments. This study contributes to theory and practice by providing a nuanced understanding of boundary conditions surrounding CEO long-term compensation, and decisions CEOs make vis-à-vis IT capital investments.
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Trifunovic, Dejan. "Investment choice under uncertainty: A review essay." Ekonomski anali 50, no. 167 (2005): 141–70. http://dx.doi.org/10.2298/eka0567141t.
Повний текст джерелаАнотація:
An investment opportunity whose return is perfectly predictable, hardly exists at all. Instead, investor makes his decisions under conditions of uncertainty. Theory of expected utility is the main analytical tool for description of choice under uncertainty. Critics of the theory contend that individuals have bounded rationality and that the theory of expected utility is not correct. When agents are faced with risky decisions they behave differently, conditional on their attitude towards risk. They can be risk loving, risk averse or risk neutral. In order to make an investment decision it is necessary to compare probability distribution functions of returns. Investment decision making is much simpler if one uses expected values and variances instead of probability distribution functions.
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Quin, S., and G. E. O. Widera. "Uncertainty Analysis in Quantitative Risk Assessment." Journal of Pressure Vessel Technology 118, no. 1 (February 1, 1996): 121–24. http://dx.doi.org/10.1115/1.2842154.
Повний текст джерелаАнотація:
Of the quantitative approaches applied to inservice inspection, failure modes, effects,criticality analysis (FMECA) methodology is recommended. FMECA can provide a straightforward illustration of how risk can be used to prioritize components for inspection (ASME, 1991). But, at present, it has two limitations. One is that it cannot be used in the situation where components have multiple failure modes. The other is that it cannot be used in the situation where the uncertainties in the data of components have nonuniform distributions. In engineering practice, these two situations exist in many cases. In this paper, two methods based on fuzzy set theory are presented to treat these problems. The methods proposed here can be considered as a supplement to FMECA, thus extending its range of applicability.
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Šrédl, K. "Behaviour of subjects in risk markets." Agricultural Economics (Zemědělská ekonomika) 56, No. 5 (June 1, 2010): 224–30. http://dx.doi.org/10.17221/67/2009-agricecon.
Повний текст джерелаАнотація:
Consumer's behaviour is described mostly by the neoclassical theory in the framework of cardinalistic and ordinalistic models which involve the methodological individualism, the concept of rationalism, the equilibrium and the perfect information of consumer. Consumer in the financial actives market decides in a similar way. Consumer can make decisions also uder the condition of risk and uncertainty.
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Yang, Shiyuan, Jiapeng Wang, and Hengfei Yang. "Evidence Theory based Uncertainty Design Optimization for Planetary Gearbox in Wind Turbine." Journal of Advances in Applied & Computational Mathematics 9 (May 24, 2022): 86–102. http://dx.doi.org/10.15377/2409-5761.2022.09.7.
Повний текст джерелаАнотація:
The planetary gearbox is an important part of the wind turbine. There are many random uncertain factors in the process of design, production, installation, and use, and these uncertain factors greatly influence the service life and reliability of the planetary gearbox. Therefore, the influence of uncertain factors needs to be considered in the design process to reduce the risk of failure. In this paper, an uncertainty design optimization method based on evidence theory is proposed, which can consider both interval variables and random variables in the optimization process. Then the megawatt wind turbine planetary gearbox is taken as the research object to analyze its uncertainty sources. Finally, the planetary gearbox is optimized by the proposed method. By comparing the results, the design scheme obtained by the method proposed in this paper is more reliable.
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Alhabeeb, M. J. "Risk and Uncertainty Revisited: A Clarification of Theory and Application." International Journal of Economics and Finance 14, no. 1 (November 28, 2021): 1. http://dx.doi.org/10.5539/ijef.v14n1p1.
Повний текст джерелаАнотація:
In addition to the obvious public confusion and lack of distinction between the terms, risk and uncertainty and other related concepts, the interchangeable use seems to seep into the academic and professional research. According to a 2018 study by De Groot and Thurik, it was reported that 88.3% of articles in this topic, across the related fields, did not adhere to the distinction between risk and uncertainty, rendering all the undesirable theoretical and empirical consequences. This paper is intended to revisit the concepts of risk and uncertainty, not only clarifying the meaning and use of the terms, but also shedding a light on differentiating all the related concepts. The focus is on risk, being the core element directly related to the success and failure of all financial and managerial decision making. The approach is not only conceptual, but also supported by mathematical and numerical applications.
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Schilirò, Daniele. "Economics versus Psychology. Risk, Uncertainty and the Expected Utility Theory." Journal of Mathematical Economics and Finance 3, no. 1 (August 25, 2017): 77. http://dx.doi.org/10.14505//jmef.v3.1(4).04.
Повний текст джерелаАнотація:
The present contribution examines the emergence of expected utility theory by John von Neumann and Oskar Morgenstern, the subjective the expected utility theory by Savage, and the problem of choice under risk and uncertainty, focusing in particular on the seminal work “The Utility Analysis of Choices involving Risk” (1948) by Milton Friedman and Leonard Savage to show how the evolution of the theory of choice has determined a separation of economics from psychology.
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Soundappan, Prabhu, Efstratios Nikolaidis, Raphael T. Haftka, Ramana Grandhi, and Robert Canfield. "Comparison of evidence theory and Bayesian theory for uncertainty modeling." Reliability Engineering & System Safety 85, no. 1-3 (July 2004): 295–311. http://dx.doi.org/10.1016/j.ress.2004.03.018.
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Li, Peixuan, Meilin Wen, Tianpei Zu, and Rui Kang. "A Joint Location–Allocation–Inventory Spare Part Optimization Model for Base-Level Support System with Uncertain Demands." Axioms 12, no. 1 (January 1, 2023): 46. http://dx.doi.org/10.3390/axioms12010046.
Повний текст джерелаАнотація:
This paper copes with a joint Location-Allocation-Inventory problem in a three-echelon base-level spare part support system with epistemic uncertainty in uncertain demands of bases. The aim of the paper is to propose an optimization model under the uncertainty theory to minimize the total cost, which integrates crucial characterizations of the inventory control decisions and the location-allocation scheme arrangement under a periodic review order-up-to-S (T, S) policy. Uncertainty theory is introduced in this paper to characterize epistemic uncertainty, where demands are treated as uncertain variables and stockout loss is represented by value-at-risk in uncertain measurement. To solve the original uncertain optimization model, an equivalent deterministic model is derived and addressed by an improved bilevel genetic algorithm. Moreover, the proposed models and algorithm are encoded into numerical examples for supply chain programming. The results highlight the applicability of the model and the algorithm’s effectiveness in approaching the optimal solution compared with traditional genetic algorithm. Sensitivity analyses are further made for the impacts of review time and inventory capacity on different cost components.
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GULKO, LES. "THE ENTROPY THEORY OF BOND OPTION PRICING." International Journal of Theoretical and Applied Finance 05, no. 04 (June 2002): 355–83. http://dx.doi.org/10.1142/s021902490200147x.
Повний текст джерелаАнотація:
An informationally efficient price keeps investors as a group in the state of maximum uncertainty about the next price change. The Entropy Pricing Theory (EPT) captures this intuition and suggests that, in informationally efficient markets, perfectly uncertain market beliefs must prevail. When the entropy functional is used to index collective market uncertainty, then the entropy-maximizing consensus beliefs must prevail. The EPT resolves the ambiguity of arbitrage-free valuation in incomplete markets. The EPT produces a new bond option model that is similar to Black–Scholes' with the lognormal distribution replaced by a beta distribution. Unlike alternative models, the beta model is valid for arbitrary term structure dynamics and for arbitrary credit risk of the underlying bonds. Option replication and hedging under the beta model accounts for random changes in the underlying bond price, price volatility and short-term interest rates.
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Kharytonova, O. O. "Duality theory under model uncertainty for non-concave utility functions." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2019): 50–56. http://dx.doi.org/10.17721/1812-5409.2019/4.6.
Повний текст джерелаАнотація:
The main goal for this paper is to study the robust utility maximization functional, i.e. sup_{X\in\Xi(x)} inf_{Q\in\mathsf{Q}} E_Q [U(X_T)]; of the terminal wealth in complete market models, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In the previous literature, this problem was studied for strictly concave utility functions and we extended existing results for non-concave utility functions by considering their concavization.
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Schultz, Wolfram, Kerstin Preuschoff, Colin Camerer, Ming Hsu, Christopher D. Fiorillo, Philippe N. Tobler, and Peter Bossaerts. "Explicit neural signals reflecting reward uncertainty." Philosophical Transactions of the Royal Society B: Biological Sciences 363, no. 1511 (October 2008): 3801–11. http://dx.doi.org/10.1098/rstb.2008.0152.
Повний текст джерелаАнотація:
The acknowledged importance of uncertainty in economic decision making has stimulated the search for neural signals that could influence learning and inform decision mechanisms. Current views distinguish two forms of uncertainty, namely risk and ambiguity, depending on whether the probability distributions of outcomes are known or unknown. Behavioural neurophysiological studies on dopamine neurons revealed a risk signal, which covaried with the standard deviation or variance of the magnitude of juice rewards and occurred separately from reward value coding. Human imaging studies identified similarly distinct risk signals for monetary rewards in the striatum and orbitofrontal cortex (OFC), thus fulfilling a requirement for the mean variance approach of economic decision theory. The orbitofrontal risk signal covaried with individual risk attitudes, possibly explaining individual differences in risk perception and risky decision making. Ambiguous gambles with incomplete probabilistic information induced stronger brain signals than risky gambles in OFC and amygdala, suggesting that the brain's reward system signals the partial lack of information. The brain can use the uncertainty signals to assess the uncertainty of rewards, influence learning, modulate the value of uncertain rewards and make appropriate behavioural choices between only partly known options.
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Emmett, Ross B. "The writing and reception of Risk, Uncertainty and Profit." Cambridge Journal of Economics 45, no. 5 (April 30, 2021): 883–900. http://dx.doi.org/10.1093/cje/beab005.
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Abstract Risk, Uncertainty and Profit was published in 1921, but started as the doctoral thesis ‘A Theory of Business Profit,’ defended in 1916. The first half of the paper examines the changes in organization and argument that Knight undertook between completing the thesis defense and the book’s publication five years later. The reorganization helped Knight focus attention on uncertainty as the most important aspect of economic life standing between the worlds of perfect and imperfect competition, and to explore more of its implications for both price theory and entrepreneurial judgment. The second half of the paper carries the story forward by examining the reception Risk, Uncertainty and Profit received from 1921 until Knight’s retirement in the early 1950s. The study of its reception uses a database of citations of Knight’s book in economics journals found through a JSTOR search. While Knight’s book is remembered today mostly for its introduction of uncertainty, in the economics literature the book’s treatment of basic price theory is more frequently cited, especially in the leading economics journals of the interwar period. The citation data indicates that the role of Risk, Uncertainty and Profit in economics education at the London School of Economics and the University of Chicago extended and expanded the book’s impact.
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Bu, Liangtao, and Hui Yue. "Quality Risk Perception of Rectification and Reinforcement in a High-Rise Building under Uncertainty." Buildings 14, no. 3 (March 13, 2024): 774. http://dx.doi.org/10.3390/buildings14030774.
Повний текст джерелаАнотація:
There are many complex and uncertain factors in the process of building rectification and reinforcement that can easily lead to construction quality failures. This study develops a novel hybrid risk analysis approach to perceive the construction quality risk under uncertainty by integrating the extension theory (ET), the cloud model (CM), the Dempster–Shafer (D-S) evidence theory and the dynamic Bayesian network (DBN). The extended cloud model (ECM) combining the ET and the CM is not only effective in avoiding information loss, but is also capable of dealing with the ambiguity and randomness in risk assessment. The ECM is employed to construct the basic probability assignments (BPA) of risk factors across different risk states. The improved D-S evidence theory considering the expert importance coefficient is used for the fusion of expert judgments. A DBN model integrating monitoring indicators is established to predict the dynamics of overall quality risk during rectification and reinforcement. Then, the measured data of settlement difference and settlement rate are fed back to the DBN model to update the risk assessment results in real time. Finally, a case study of the rectification and reinforcement in a high-rise building is taken to verify the feasibility and validity of the developed risk analysis approach. The risk assessment results better reflect the unexpected risk events in actual construction. The proposed approach provides a research paradigm for quality risk assessment of similar rectification and reinforcement projects.
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Wu, Wenbo, Tianji Zou, Dong Guo, Lu Zhang, Ke Wang, and Xuzhi Li. "Fault Diagnosis for China Space Station Circulating Pumps: Prototypical Network with Uncertainty Theory." Symmetry 15, no. 4 (April 13, 2023): 903. http://dx.doi.org/10.3390/sym15040903.
Повний текст джерелаАнотація:
Methods for fault diagnosis based on metric learning, in which a query sample is classified by picking the closest prototype from the support set based on their feature similarities, have been the subject of many studies. In real-world applications of in-orbit products, such as circulating pumps, the computation of similarity between different pairs is prone to different degrees of inaccuracy, especially epistemic uncertainty. Knowing and considering the uncertainty of similarity may improve fault detection accuracy. This article provides a unique approach to fault diagnosis based on Prototypical Network (Pro-Net) and Uncertainty Theory. In particular, we use epistemic uncertainty by altering the representation of prototypes from a deterministic scalar to an uncertain representation. To assess the similarity between a query and the prototypes in a support set, we calculate the uncertain distance between the pairs using cross-entropy. Experiments with symmetrical structures reveal that our proposed method significantly enhances classification precision and achieves state-of-the-art performance. It improves the reliability of fault diagnosis and reduces the risk of making erroneous judgments in safety-critical systems, decreasing the possibility of adverse consequences.
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Bougofa, M., A. Bouafia, A. Baziz, S. Aberkane, R. Kharzi, and A. Bellaouar. "Risk analysis-based reliability assessment approach under epistemic uncertainty using a dynamic evidential network." IOP Conference Series: Earth and Environmental Science 896, no. 1 (November 1, 2021): 012035. http://dx.doi.org/10.1088/1755-1315/896/1/012035.
Повний текст джерелаАнотація:
Abstract Probabilistic modeling is widely used in industrial practices, particularly for assessing complex systems’ safety, risk analysis, and reliability. Conventional risk analysis methodologies generally have a limited ability to deal with dependence, failure behavior, and epistemic uncertainty such as parameter uncertainty. This work proposes a risk-based reliability assessment approach using a dynamic evidential network (DEN). The proposed model integrates Dempster-Shafer theory (DST) for describing parameter uncertainty with a dynamic Bayesian network (DBN) for dependency representation and multi-state system reliability. This approach treats uncertainty propagation across conditional belief mass tables (CBMT). According to the results acquired in an interval, it is possible to analyze the risk like interval theory, and ignoring this uncertainty may lead to prejudiced results. The epistemic uncertainty should be adequately defined before performing the risk analysis. A case study of a level control system is used to highlight the methodology’s ability to capture dynamic changes in the process, uncertainty modeling, and sensitivity analysis that can serve decision making.
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Zhang, Qingyuan, Rui Kang, and Meilin Wen. "A new method of level-2 uncertainty analysis in risk assessment based on uncertainty theory." Soft Computing 22, no. 17 (June 19, 2018): 5867–77. http://dx.doi.org/10.1007/s00500-018-3337-0.
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Beissner, Patrick. "Coherent-Price Systems and Uncertainty-Neutral Valuation." Risks 7, no. 3 (September 17, 2019): 98. http://dx.doi.org/10.3390/risks7030098.
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This paper considers fundamental questions of arbitrage pricing that arises when the uncertainty model incorporates ambiguity about risk. This additional ambiguity motivates a new principle of risk- and ambiguity-neutral valuation as an extension of the paper by Ross (1976) (Ross, Stephen A. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13: 341–60). In the spirit of Harrison and Kreps (1979) (Harrison, J. Michael, and David M. Kreps. 1979. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20: 381–408), the paper establishes a micro-economic foundation of viability in which ambiguity-neutrality imposes a fair-pricing principle via symmetric multiple prior martingales. The resulting equivalent symmetric martingale measure set exists if the uncertain volatility in asset prices is driven by an ambiguous Brownian motion.
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Paul Makesh, Dr A. "ANALYSIS OF UNCERTAINTY IN A CONSTRUCTION PROJECT." YMER Digital 20, no. 12 (December 15, 2021): 324–32. http://dx.doi.org/10.37896/ymer20.12/29.
Повний текст джерелаАнотація:
This article presents the analysis of uncertainty and effectiveness in cost to construction project. Theoretical part describes various definitions of uncertainty, risk both with there sources as calculation bias, information ambiguity and data inaccuracy in construction projects. Main analysis is connected with the project's appraisal phase and its stages were the detailed information is the crucial factor for correct decision- making procedures under uncertainty and risk. Consequently this article is presenting various types risk what are undistinguishable from uncertainty circumstances in construction. After the description of risk and uncertainty types list of solutions were prepared. Application of the suggested risk and uncertainty extenuating techniques in practice was shown as analysis of precision and bias dependence with available information at different stages of appraisal phase.It is emphasized on uncertainty and risk management problem in the construction's decision- making. Recently methods based on the utility theory, game theory, statistical distribution and probability, were improved and adjusted due to decision-making needs in construction. That is why the model with implemented multiple-criteria approaches is suggested both as a tool for dealing with the uncertainty and risk problems and to meet the needs of project managers in appraisal phase.
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Radonjic, Ognjen. "Fundamental uncertainty and Keynes' probability theory." Theoria, Beograd 50, no. 4 (2007): 35–55. http://dx.doi.org/10.2298/theo0704035r.
Повний текст джерелаАнотація:
Within economic system agents daily make decisions. Those decisions are based on their expectations regarding future. Therefore, theoretical assumption about what do rational decision-makers really know about future and could agents make relatively reliable forecasts has colossal importance. Namely this assumption critically determines theoretical modeling of decision-making process. In economic theory we can make distinction between two opposite and irreconcilable standpoints on this issue. According to proponents of the Subjective Probability and the Rational Expectations Hypothesis future can be predicted exactly, that is, agents are able to mathematically calculate future precisely and to express it in terms of numbers. Consistently behavior of individual agent and society in aggregate can be predicted with great precision. On the other hand, Keynes, first economist who made clear distinction between risk and uncertainty, argued that past experiences and statistical analysis of past data were not reliable guide to future and that behavior of individual agents and society in aggregate could not be neither calculated exactly nor precisely predicted. Consequently, theoretical implications regarding decision-making and behavior of aggregate economic system of the two opposite standpoints are completely different.
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Deng, Xue, and Cuirong Huang. "Mean-entropy uncertain portfolio with risk curve and total mental accounts under multiple background risks." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 539–61. http://dx.doi.org/10.3233/jifs-202256.
Повний текст джерелаАнотація:
In the previous uncertain portfolio literature on background risk and mental account, only a general background risk and a few kinds of mental accounts were considered. Based on the above limitations, on the one hand, the multiple background risks are defined by linear weighting of different background asset risks in this paper; on the other hand, the total nine kinds of mental accounts are comprehensively considered. Especially, the risk curve is regarded as the risk measurement of different mental accounts for the first time. Under the framework of uncertainty theory, a novel mean-entropy portfolio model with risk curve and total mental accounts under multiple background risks is constructed. In addition, transaction fees, chance constraint, upper and lower limits and initial wealth constraints are also considered in our proposed model. In theory, the equivalent forms of the models with different uncertainty distributions (general, normal and zigzag) are presented by three theorems. Simultaneously, the corresponding concrete expressions of risk curves are obtained by another three theorems. In practice, two numerical examples verify the feasibility and effectiveness of our proposed model. Finally, we can obtain the following unique and meaningful findings: (1) investors will underestimate the potential risk if they ignore the existence of multiple background risks; (2) with the increase of the return threshold, the return of the sub-portfolio will inevitably increase, but investors also bear the risk that the risk curve is higher than the confidence curve at this time.
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Wang, Xiangpei, and Chang Yuan. "Research on Asian Option Pricing Based on Uncertain Volatility." Modern Economics & Management Forum 5, no. 5 (November 6, 2024): 916. http://dx.doi.org/10.32629/memf.v5i5.2883.
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In this paper, we study the impact of introducing uncertainty volatility into Asian options pricing, with emphasis on the use of Hamilton-Jacobi-Bellman (HJB) equation. The traditional Asian option pricing model usually assumes that volatility is known and constant, but in the actual market, volatility is often uncertain and volatile. This paper first reviews the pricing theory of Asian options, and then introduces the hypothesis of uncertain volatility. By constructing the HJB equation based on uncertainty volatility, a new pricing method is proposed and verified by numerical simulation. The results show that after the introduction of uncertain volatility, the price range of Asian options expands significantly, reflecting higher market uncertainty and risk.
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Wang, Jian, Jiansheng Guo, Mingfa Zheng, Zheng MuRong, and Zhengxin Li. "Research on a novel minimum-risk model for uncertain orienteering problem based on uncertainty theory." Soft Computing 23, no. 12 (January 18, 2019): 4573–84. http://dx.doi.org/10.1007/s00500-018-03699-1.
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Jedynak, Piotr, and Sylwia Bąk. "Understanding Uncertainty and Risk in Management." Journal of Intercultural Management 12, no. 1 (March 1, 2020): 12–35. http://dx.doi.org/10.2478/joim-2020-0030.
Повний текст джерелаАнотація:
AbstractObjective: The purpose of this text is to identify approaches to defining and subsequently reviewing the definitions of uncertainty and risk as interdisciplinary terms which are of key importance in modern management.Methodology: The work is theoretical. The main method used in the research process was the analysis of scientific literature. A one-dimensional logical classification method was also used, in order to categorize approaches to defining uncertainty and risk, satisfying the exhaustive and mutually exclusive criteria in the selection of categories of approaches.Findings: The main results of the work are: 1) identification of approaches to defining uncertainty and risk, 2) interdisciplinary review of definitions of uncertainty and risk indicating the criteria to distinguish between the two, and 3) determination of the meaning of the terms uncertainty and risk in modern management.Value Added: Considering the approaches to defining uncertainty and risk taken from many fields and disciplines of science, this text is a compendium of theoretical knowledge for the proper understanding and meaning of these concepts in management.Recommendations: The research findings can have implications for both management theory as well as the practice of organization management.
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Ke, Hua, Yong Wu, and Hu Huang. "Competitive Pricing and Remanufacturing Problem in an Uncertain Closed-Loop Supply Chain with Risk-Sensitive Retailers." Asia-Pacific Journal of Operational Research 35, no. 01 (February 2018): 1850003. http://dx.doi.org/10.1142/s0217595918500033.
Повний текст джерелаАнотація:
Nowadays, pricing and remanufacturing problems under uncertain markets have gained increasing attention from both industrial and academic fields. In the literature, it is generally assumed that all the channel members are risk-neutral, ignoring the influences of channel members’ risk attitudes in the face of dynamic market. This paper focuses on a pricing problem in a closed-loop supply chain (CLSC) with two competitive risk-sensitive retailers under uncertain environment. The uncertainty is associated with the recycling costs, consumer demands and remanufacturing costs. Due to the dynamic market, supply chain managers may be unable to collect enough historical data to estimate these demands and costs when making pricing and remanufacturing decisions. In such cases, experts’ estimations are usually employed to describe these uncertain parameters. To deal with these human estimations, an uncertainty theory-based model is proposed. Based on the equilibrium results, how the retailers’ risk sensitivity and human estimations (uncertain degrees) affect the prices and profits is analyzed. It is found that both the retailers will get lower profits while the manufacturer will gain more profit when either of the two retailers becomes more risk-averse. We also find that a higher level of uncertainty in the supply chain will induce a higher collecting rate.
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Fried, Barbara H. "Facing Up To Risk." Journal of Legal Analysis 10 (2018): 175–98. http://dx.doi.org/10.1093/jla/laz003.
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AbstractBy banishing decision-making in the face of uncertainty (risk) to the margins of tort theory, nonconsequentialist legal philosophers have obscured the quotidian, unavoidable, and ubiquitous tradeoffs we face in almost every arena of life. This article explores the historical antecedents of the marginalization of risk in contemporary moral philosophy, and details how legal philosophers have deflected the challenge that risk poses to any nonconsequentialist theory of tort liability.
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Alexandru, Tărăbîc Andrei. "Defining the Concept of Risk Applied in Entrepreneurship. Conceptual Delimitation Risk - Entrepreneurial Uncertainty." European Review Of Applied Sociology 12, no. 18 (June 1, 2019): 43–46. http://dx.doi.org/10.1515/eras-2019-0004.
Повний текст джерелаАнотація:
AbstractEven though in many cases the terms of risk and uncertainty are similar, they have to be delimited to understand the meaning of each, individual, as accurately as possible. The two terms are combined in different situations. No matter how well the risk is managed, uncertainty cannot be removed because all possible situations and interdependencies cannot be taken into account. Thus, a source of risk can be considered uncertainty in itself if it is based on poor quality information about the actual internal or external situation of the company. Also, in my conclusion, traditional financial theory distinguishes between systematic risk and particular risk, which reaches the company’s overall risk. Investors can reduce total risk with the two primary risk management instruments, namely diversification and asset allocation.
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Limbourg, P., R. Savić, J. Petersen, and H.-D. Kochs. "Modelling uncertainty in fault tree analyses using evidence theory." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 222, no. 3 (September 2008): 291–302. http://dx.doi.org/10.1243/1748006xjrr142.
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Moura, Stephanie Tonn Goulart, Christian Daniel Falaster, Christine Elena Bianchi, Érica de Souza Mazato, and Laura Taysa Espig. "How Institutions Shape Uncertainty and Risk." Internext 16, no. 3 (September 1, 2021): 238–51. http://dx.doi.org/10.18568/internext.v16i3.604.
Повний текст джерелаАнотація:
Purpose: The study proposes a conceptual framework on how institutions influence risk and uncertainty. Beyond the nuances in defining the concepts in the existing literature, the role of institutions in shaping risks and uncertainties remains understudied. This paper adopts the new institutional economics (NIE) perspective to revisit the concepts of risk and uncertainty and provide a deeper reflection about its interactions with formal and informal institutions. Method: Our conceptual model is based on four propositions that support a theoretical explanation about the relationships between institutions and uncertainties, institutions and risks, and uncertainties and risks. Findings: While formal institutions have a primary role in reducing uncertainties, informal institutions can be seen as a source of risk. These findings imply firms’ strategic decisions. In this regard, we also provide a research agenda for future empirical studies in the area. Originality/value: The study highlights the importance of institutions for companies to deal with risk and uncertainties. The institutions have a primary role in defining the “known part” of the uncertainty, allowing the companies to evaluate the different scenarios for decision-making. Theoretical/Methodological Contributions: This study differentiates risk and uncertainty interaction according to institutional theory. Additionally, we offer an academic discussion of how formal and informal institutions can shape risks and uncertainties.
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Cao, Xin, Chongshi Gu, and Erfeng Zhao. "Uncertainty Instability Risk Analysis of High Concrete Arch Dam Abutments." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6037125.
Повний текст джерелаАнотація:
The uncertainties associated with concrete arch dams rise with the increased height of dams. Given the uncertainties associated with influencing factors, the stability of high arch dam abutments as a fuzzy random event was studied. In addition, given the randomness and fuzziness of calculation parameters as well as the failure criterion, hazard point and hazard surface uncertainty instability risk ratio models were proposed for high arch dam abutments on the basis of credibility theory. The uncertainty instability failure criterion was derived through the analysis of the progressive instability failure process on the basis of Shannon’s entropy theory. The uncertainties associated with influencing factors were quantized by probability or possibility distribution assignments. Gaussian random theory was used to generate random realizations for influence factors with spatial variability. The uncertainty stability analysis method was proposed by combining the finite element analysis and the limit equilibrium method. The instability risk ratio was calculated using the Monte Carlo simulation method and fuzzy random postprocessing. Results corroborate that the modeling approach is sound and that the calculation method is feasible.
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Zhao, Yuan Xiang, and Yan Min Zhang. "Floodwater Utilization Integrated Risk Evaluation Model Based on D-S Evidential Theory." Advanced Materials Research 599 (November 2012): 787–94. http://dx.doi.org/10.4028/www.scientific.net/amr.599.787.
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According to more and more serious problems of water scarcity, water pollution and deterioration of water environment in homeland, floodwater utilization becomes an important content in flood management and a critical solution for above problems. However, because of the uncertainty and subjective factor in the hydrology and water resources systems, floodwater utilization is a risk decision-making and the evaluation on the risk reasonably becomes an important decision-making reasoning problem. Traditional risk evaluation method considers uncertainty of things, but has little study on incompleteness of things and uncertainty of human’s subjective decision. An integrated risk evaluation model of floodwater utilization is presented based on D-S theory which can solve these problems successfully and with a case study, some benefit conclusions are provided.
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FÖLLMER, HANS, and IRINA PENNER. "MONETARY VALUATION OF CASH FLOWS UNDER KNIGHTIAN UNCERTAINTY." International Journal of Theoretical and Applied Finance 14, no. 01 (February 2011): 1–15. http://dx.doi.org/10.1142/s0219024911006231.
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The classical valuation of an uncertain cash flow in discrete time consists in taking the expectation of the sum of the discounted future payoffs under a fixed probability measure, which is assumed to be known. Here we discuss the valuation problem in the context of Knightian uncertainty. Using results from the theory of convex risk measures, but without assuming the existence of a global reference measure, we derive a robust representation of concave valuations with an infinite time horizon, which specifies the interplay between model uncertainty and uncertainty about the time value of money.