Rank-dependent Expected Utility Theory Research Articles

Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory

This paper investigates two optimal portfolio selection problems for a rank-dependent utility investor who needs to manage his risk exposure: one with a single Value-at-Risk (VaR) constraint and the other with joint VaR and portfolio insurance constraints. The two models generalize existing models under expected utility theory and behavioral theory. The martingale method, quantile formulation, and relaxation method are used to obtain explicit optimal solutions. We have specifically identified an equivalent condition under which the VaR constraint is effective. A numerical analysis is carried out to demonstrate theoretical results, and additional financial insights are presented. We find that, in bad market states, the risk of the optimal investment outcome is reduced when compared to existing models without or with one constraint.

Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation

We provide an axiomatic foundation for the measurement of correlation diversification in a one-period portfolio model. We propose a set of eight desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures. We study the compatibility of our axioms with rank-dependent expected utility theory. We also test them against the two most frequently used methods for measuring correlation diversification in portfolio theory: portfolio variance and the diversification ratio. Lastly, we provide an example of a functional representation of a coherent correlation diversification measure.

Optimal Portfolio Selection With VaR and Portfolio Insurance Constraints Under Rank-Dependent Expected Utility Theory

This paper investigates two optimal portfolio selection problems for a rank-dependent utility investor who needs to manage his risk exposure: one with a single Value-at-Risk (VaR) constraint and the other with joint VaR and portfolio insurance constraints. The two models generalize existing models under expected utility theory and behavioral theory. To obtain explicit optimal solutions, the martingale method, quantile formulation, and relaxation method are used. We have specifically identified an equivalent condition under which the VaR constraint is effective. A numerical analysis is carried out to demonstrate theoretical results, and additional financial insights are presented. We find that, in bad market states, the risk of the optimal investment outcome is reduced when compared to existing models without or with one constraint.

The Weapon of the Weak: An Analysis of RDEU Game in the Conflict of Farmland Expropriation under the Influence of Emotion

During land expropriation, it is difficult to form a real antagonistic relationship between farmers and the local Government due to disparities, which means the confrontations between them are difficult to administer. The confrontation between both parties could lead to the distortion of the farmers’ resisting logic, who are supposed to be in a vulnerable position. Hence, the farmers are not necessarily in a weak position; sometimes, they even have advantages compared with the local governments. Through the combination of Quiggin’s rank-based expected utility theory and evolutionary game theory, this paper constructs a conflict-induced game mechanism Rank-Dependent Expected Utility Theory (RDEU) evolutionary game model and discusses the evolution law of strategic behavior of land-expropriated farmers and local governments under the influence of emotion. The software simulation results show that when the farmers at the weak side think that the probability of the government adopting the strong strategy is higher than a certain cut-off point, the farmers will use the weapon of the weak to release the signal that endangers the order and force the government to adopt a compromise strategy by utilizing authoritative preference for stability. Through the interaction of heterogeneous beliefs between farmers and the government, the game of land expropriation will form an evolutionary stable equilibrium.

How to involve individuals in personal carbon trading? A game model taking into account the heterogeneous emotions of government and individuals

The implementation of personal carbon trading (PCT) scheme is urgently required in the context of low-carbon development. It is a key issue and a difficult problem for government to design the pattern of involving individuals into PCT scheme. Based on the rank-dependent expected utility theory, game model and numerical simulation were employed to analyse the influences of the heterogeneous emotions of government and individuals on their equilibrium strategies about the pattern of implementing PCT scheme. The findings show that the emotions of government and individuals cannot influence the equilibrium of pure strategies, but do affect the equilibrium of the mixed strategy. Further analysis shows that the strategy of government can be influenced by individuals’ emotions, and government will move towards the “mandatory pattern” strategy when individuals are optimistic and towards the “voluntary pattern” strategy when individuals are pessimistic. Additionally, the strategy of individuals can be affected by government’s emotions, and individuals will move towards “rejection” strategy when government is optimistic and towards the “participation” strategy when government is pessimistic. Therefore, the most expected emotional state for government is to remain pessimistic and to keep individuals optimistic. This study demonstrated the effects of the heterogeneous emotions of government and individuals on the equilibrium strategies about the pattern of implementing PCT scheme, provided policy suggestions for the pattern of implementing PCT scheme, and contributed to the successful implementation of future PCT scheme as well as the achievement of global carbon emissions targets.

Risk measures based on behavioural economics theory

Coherent risk measures (Artzner et al. in Math. Finance 9:203–228, 1999) and convex risk measures (Follmer and Schied in Finance Stoch. 6:429–447, 2002) are characterized by desired axioms for risk measures. However, concrete or practical risk measures could be proposed from different perspectives. In this paper, we propose new risk measures based on behavioural economics theory. We use rank-dependent expected utility (RDEU) theory to formulate an objective function and propose the smallest solution that minimizes the objective function as a risk measure. We also employ cumulative prospect theory (CPT) to introduce a set of acceptable regulatory capitals and define the infimum of the set as a risk measure. We show that the classes of risk measures derived from RDEU theory and CPT are equivalent, and they are all monetary risk measures. We present the properties of the proposed risk measures and give sufficient and necessary conditions for them to be coherent and convex, respectively. The risk measures based on these behavioural economics theories not only cover important risk measures such as distortion risk measures, expectiles and shortfall risk measures, but also produce new interesting coherent risk measures and convex, but not coherent risk measures.

Credit markets with imperfect information: Risk-aversion versus pessimism

Stiglitz and Weiss (1981) credit rationing is embedded within rank dependent expected utility theory. Our results show that sufficient pessimism or sufficient risk-aversion by borrowers may eliminate adverse selection. Moreover, lender optimism may eliminate credit rationing even when adverse selection exists.

À la recherche de la signification perdue du paradoxe d’Allais

Dans « Le paradoxe d’Allais. Comment lui rendre sa signification perdue ? », Philippe Mongin [2014] propose une image contestable, parce qu’abusivement rassurante, de la rationalité des sujets participant aux expériences de MacCrimmon et Larsson [1979]. Nous montrons cela en restituant les données des auteurs pour l’effet de conséquence commune et l’effet de rapport commun (deux paradoxes d’Allais), que Mongin assimile, bien qu’il distingue ces deux effets. Deux tendances dans les données nous conduisent à rejoindre Mongin pour conclure que ces expériences sont une source d’inspiration fructueuse pour la théorie de la décision, ce que nous illustrons brièvement par le rôle qu’elles ont joué dans l’apparition de l’utilité espérée dépendante du rang et dans le tournant interindividuel en psychologie cognitive de la décision.

Diversification preferences in the theory of choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von Neumann–Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper analyzes axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.

Diversification Preferences in the Theory of Choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper analyzes axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. The article covers model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.

Comparative Loss Aversion: Some New Behavioral Implications

This paper proposes a new loss aversion coefficient for decision makers. Considering this loss aversion coefficient and Shalev’s (2002) perceptive utility function, we define a new version of rank-dependent expected utility theory. Our main results extend the restrictions of comparative loss aversion, and reveal the behavioral implications of comparative loss aversion. The new loss aversion coefficient is well defined as a measure of degree of loss aversion. Our main findings of comparative loss aversion can also be applied to welfare, health, insurance and other topical economic problems. Key words: Loss aversion coefficient; Comparative loss aversion; Rank-dependent expected utility; Decision making under risk

Improving resource allocation strategies against human adversaries in security games: An extended study

Stackelberg games have garnered significant attention in recent years given their deployment for real world security. Most of these systems, such as ARMOR, IRIS and GUARDS have adopted the standard game-theoretical assumption that adversaries are perfectly rational, which is standard in the game theory literature. This assumption may not hold in real-world security problems due to the bounded rationality of human adversaries, which could potentially reduce the effectiveness of these systems.In this paper, we focus on relaxing the unrealistic assumption of perfectly rational adversary in Stackelberg security games. In particular, we present new mathematical models of human adversariesʼ behavior, based on using two fundamental theory/method in human decision making: Prospect Theory (PT) and stochastic discrete choice model. We also provide methods for tuning the parameters of these new models. Additionally, we propose a modification of the standard quantal response based model inspired by rank-dependent expected utility theory. We then develop efficient algorithms to compute the best response of the security forces when playing against the different models of adversaries. In order to evaluate the effectiveness of the new models, we conduct comprehensive experiments with human subjects using a web-based game, comparing them with models previously proposed in the literature to address the perfect rationality assumption on part of the adversary.Our experimental results show that the subjectsʼ responses follow the assumptions of our new models more closely than the previous perfect rationality assumption. We also show that the defender strategy produced by our new stochastic discrete choice model outperform the previous leading contender for relaxing the assumption of perfect rationality. Furthermore, in a separate set of experiments, we show the benefits of our modified stochastic model (QRRU) over the standard model (QR).11This paper significantly extends our previous conference paper (Yang et al., 2011) [1] by providing (i) new methods for setting parameters of the Prospect Theory model; (ii) an additional variant of Quantal Response model and a new algorithm to compute defender strategies against the new model; (iii) a more comprehensive set of experiments which includes multiple new algorithms and updated settings for the algorithms; (iv) new analysis of the robustness of different defender strategies and the predictive accuracy of different models; (v) additional discussion of related work.

Modelling travellers’ risky choice in a revealed preference context: a comparison of EUT and non-EUT approaches

Recent work on risky choice modelling has sought to address the shortcomings of expected utility theory (EUT) by using non-expected utility theoretic (non-EUT) approaches. However, to date these approaches have been merely tested on stated choice data which is flexible and cheap. In this study, we empirically investigate the feasibility and validity of non-EUT approaches in a revealed preference (RP) context in which travel time distribution is extracted from observed historical travel time data, and subsequently present systematic comparisons between EUT, weighted utility theory, rank-dependent expected utility theory, and prospect theory (PT). The empirical evidence indicates that each non-EUT model has important behavioural insights to offer, moreover, EUT as well as non-EUT models can be applied to the RP context. However, the EUT and non-EUT model fits are generally similar with only PT providing a marginally improved model fit over EUT. The key findings presented in this study reinforce the importance of exploring non-EUT models within a revealed preference context before they can be applied reliably to modelling risky choices in the real world.

Rank Dependent Utility, Tax Evasion and Labor Supply

In the simple Allingham-Sandmo portfolio model of tax evasion an expected utility maximizer will cheat more than what is estimated in empirical studies. Two main types of explanation have been suggested as solutions to this puzzle: (1) Tax payers act according to some non-expected utility theory, and (2) Individual ethical norms and social stigma induce people not to cheat. In the present study we test two hypotheses within these broad explanations: (1) Tax payers are weighting subjective probabilities of being penalised according to the rank dependent utility theory, and (2) Tax payers’ beliefs about social norms have an effect on their decision to evade taxes. Our model is characterized by a simultaneous determination of tax evasion and labour supply, including the effect on tax payers of a social norm of not cheating. Using Norwegian survey data our hypotheses are corroborated. Our estimates imply that if the objective probability of being penalized is, say 3 %, the weighted probability is about 23 %. Our study provides an independent confirmation of the rank dependent expected utility theory. The model explains data 53% better than pure random choices and predicts hours worked in the regular economy, among tax evaders as well non tax evaders, rather precisely. The model is an example of a two sector choice model and the results indicate that an overall wage increase may shift labor supply away from the irregular part of the economy towards the regular.

The Distorted Theory of Rank-Dependent Expected Utility

This paper re-examines the rank-dependent expected utility theory. Firstly, we follow Quiggin's assumption (Quiggin 1982) that the transformation of cumulative distribution functions is a continuous function of the whole probability distribution to deduce the rank-dependent expected utility formula over lotteries and hence extend it to the case of general random variables. Secondly, we employ an axiomatic approach to build a distorted theory of rank-dependent expected utility. The transformation of the cumulative distribution functions is the decision weights function in the rank-dependent expected utility formula which reflects decision-makers' beliefs. We call it the distortion function which `distorts' the decision-maker's probabilities. Utilizing this distortion function, we propose a distorted independence axiom to prove the representation theorem of rank-dependent expected utility. Finally, we make direct use of the distorted independence axiom to explain the Allais paradox and the common ratio effect. We show that the inconsistency in these examples arises when the distortion function takes specific forms under the framework of the distorted independence axiom.

Accident Liability with Rank Dependence

KritV Kritische Vierteljahresschrift für Gesetzgebung und Rechtswissenschaft , Seite 160 - 171

Inverse stochastic dominance constraints and rank dependent expected utility theory

We consider optimization problems with second order stochastic dominance constraints formulated as a relation of Lorenz curves. We characterize the relation in terms of rank dependent utility functions, which generalize Yaari's utility functions. We develop optimality conditions and duality theory for problems with Lorenz dominance constraints. We prove that Lagrange multipliers associated with these constraints can be identified with rank dependent utility functions. The problem is numerically tractable in the case of discrete distributions with equally probable realizations.

Testing the Predictions of Decision Theories in a Natural Experiment when Half a Million is at Stake

In the television show Affari Tuoi an individual faces a sequence of binary choices between a risky lottery with equiprobable prizes of up to half a million euros and a monetary amount for certain. The decisions of 114 show participants are used to test the predictions of ten decision theories: risk neutrality, expected utility theory, fanning-out hypothesis (weighted utility theory, transitive skew-symmetric bilinear utility theory), (cumulative) prospect theory, regret theory, rank-dependent expected utility theory, Yaarii?½s dual model, prospective reference theory and disappointment aversion theory. Assumptions of risk neutrality and loss aversion are clearly violated, respectively, by 55% and 46% of all contestants. There appears to be no evidence of nonlinear probability weighting or disappointment aversion. Observed decisions are generally consistent with the assumption of regret aversion and there is strong evidence for the fanning-out hypothesis. Nevertheless, we find no behavioral patterns that cannot be reconciled within the expected utility framework (or prospective reference theory that gives identical predictions).

Production under Uncertainty and Choice under Uncertainty in the Emergence of Generalized Expected Utility Theory

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.

Parameter-Free Elicitation of Utility and Probability Weighting Functions

This paper proposes a two-step method to successively elicit utility functions and decision weights under rank-dependent expected utility theory and its “more descriptive” version: cumulative prospect theory. The novelty of the method is that it is parameter-free, and thus elicits the whole individual preference functional without imposing any prior restriction. This method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains. Concave utility functions are obtained for gains and convex utility functions for losses. The elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations. The data also show that the probability weighting function for losses is more “elevated” than for gains.