scholarly journals Risk Measures and Theories of Choice

2003 ◽  
Vol 9 (4) ◽  
pp. 959-991 ◽  
Author(s):  
A. Tsanakas ◽  
E. Desli
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Utility Theory ◽  
Dual Theory ◽  
Economic Theories ◽  
Special Cases ◽  
Measures Of Risk

ABSTRACTWe discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003), whereas Yaari's (1987) dual theory of choice under risk can be viewed as the source of the distortion premium principle (Denneberg, 1990; Wang, 1996). We argue that the properties of the exponential and distortion premium principles are complementary, without either of the two performing completely satisfactorily as a risk measure. Using generalised expected utility theory (Quiggin, 1993), we derive a new risk measure, which we call the distortion-exponential principle. This risk measure satisfies the axioms of convex measures of risk, proposed by Föllmer & Shied (2002a,b), and its properties lie between those of the exponential and distortion principles, which can be obtained as special cases.

scholarly journals Dynamic Portfolio Allocation, the Dual Theory of Choice and Probability Distortion Functions

2006 ◽  
Vol 36 (01) ◽  
pp. 187-217 ◽  
Author(s):  
Mahmoud Hamada ◽  
Michael Sherris ◽  
John van der Hoek
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Utility Theory ◽  
Risk Measures ◽  
Rank Order ◽  
Expected Utility Theory ◽  
Portfolio Optimisation ◽  
Normal Distribution Function ◽  
Distortion Functions ◽  
Future Outcomes

Standard optimal portfolio choice models assume that investors maximise the expected utility of their future outcomes. However, behaviour which is inconsistent with the expected utility theory has often been observed. In a discrete time setting, we provide a formal treatment of risk measures based on distortion functions that are consistent with Yaari’s dual (non-expected utility) theory of choice (1987), and set out a general layout for portfolio optimisation in this non-expected utility framework using the risk neutral computational approach. As an application, we consider two particular risk measures. The first one is based on the PH-transform and treats the upside and downside of the risk differently. The second one, introduced by Wang (2000) uses a probability distortion operator based on the cumulative normal distribution function. Both risk measures rank-order prospects and apply a distortion function to the entire vector of probabilities.

scholarly journals Dynamic Portfolio Allocation, the Dual Theory of Choice and Probability Distortion Functions

2006 ◽  
Vol 36 (1) ◽  
pp. 187-217 ◽  
Author(s):  
Mahmoud Hamada ◽  
Michael Sherris ◽  
John van der Hoek
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Utility Theory ◽  
Risk Measures ◽  
Rank Order ◽  
Expected Utility Theory ◽  
Portfolio Optimisation ◽  
Normal Distribution Function ◽  
Distortion Functions ◽  
Future Outcomes

Standard optimal portfolio choice models assume that investors maximise the expected utility of their future outcomes. However, behaviour which is inconsistent with the expected utility theory has often been observed.In a discrete time setting, we provide a formal treatment of risk measures based on distortion functions that are consistent with Yaari’s dual (non-expected utility) theory of choice (1987), and set out a general layout for portfolio optimisation in this non-expected utility framework using the risk neutral computational approach.As an application, we consider two particular risk measures. The first one is based on the PH-transform and treats the upside and downside of the risk differently. The second one, introduced by Wang (2000) uses a probability distortion operator based on the cumulative normal distribution function. Both risk measures rank-order prospects and apply a distortion function to the entire vector of probabilities.

scholarly journals Cumulative Prospect Theory Version with Fuzzy Values of Outcome Estimates

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 72
Author(s):  
Oleg Uzhga-Rebrov ◽  
Peter Grabusts
Keyword(s):  
Prospect Theory ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
Development History ◽  
Decisions Under Risk ◽  
History Of ◽  
Main Factors ◽  
Theoretical Foundations

Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in choosing a solution is modeling the decision maker’s attitude to risk. The expected utility theory was the first approach that allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of even more effective approaches to solving this problem. Currently, the most developed theory of choice with respect to decisions under risk conditions is the cumulative prospect theory. This paper presents the development history of various extensions of the original expected utility theory, and the analysis of the main properties of the cumulative prospect theory. The main result of this work is a fuzzy version of the prospect theory, which allows handling fuzzy values of the decisions (prospects). The paper presents the theoretical foundations of the proposed version, an illustrative practical example, and conclusions based on the results obtained.

Norm-Endorsement Utilitarianism and the Nature of Utility

1996 ◽  
Vol 12 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Jonathan Baron
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Interpersonal Comparison ◽  
Moral Norms ◽  
Moral Principles ◽  
Future Goals ◽  
Equal Consideration

In this article, I shall suggest an approach to the justification of normative moral principles which leads, I think, to utilitarianism. The approach is based on asking what moral norms we would each endorse if we had no prior moral commitments. I argue that we would endorse norms that lead to the satisfaction of all our nonmoral values or goals. The same approach leads to a view of utility as consisting of those goals that we would want satisfied. In the second half of the article, I examine the implication of this view for several issues about the nature of utility, such as the use of past and future goals. The argument for utilitarianism is not completed here. The rest of it requires a defense of expected-utility theory, of interpersonal comparison, and of equal consideration (see Baron, 1993; Broome, 1991).

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