Risk Aversion in Cumulative Prospect Theory

This paper characterizes the conditions for risk aversion in cumulative prospect theory where risk aversion is defined in the strong sense (Rothshild Stiglitz 1970). Under weaker assumptions than differentiability we show that risk aversion implies convex weighting functions for gains and for losses but not necessarily a concave utility function. Also, we investigate the exact relationship between loss aversion and risk aversion. We illustrate the analysis by considering two special cases of cumulative prospect theory and show that risk aversion and convex utility may coexist.

Endogenous Prospect Theory.

In previous models of (cumulative) prospect theory reference-dependence of preferences is imposed beforehand and the location of the reference point is exogenously determined. This paper provides an axiomatization of a new specification of cumulative prospect theory, termed endogenous prospect theory, where reference-dependence is derived from preference conditions and a unique reference point arises endogenously.prospect theory; reference point; diminishing sensitivity; loss aversion;

An Axiomatization of Linear Cumulative Prospect Theory with Applications to Portfolio Selection and Insurance Demand

The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of corresponding preferences in a cumulative prospect theory (CPT) framework. CPT is one of the most promising alternatives to expected utility theory since it incorporates loss aversion, and linear utility for money receives increasing attention since it is often concluded in empirical research, and employed in theoretical applications. Rabin (2000) emphasizes the importance of linear utility, and highlights loss aversion as an explanatory feature for the disparity of significant small-scale risk aversion and reasonable large-scale risk aversion. In a sense we derive a two-sided variant of Yaari s dual theory, i.e. nonlinear probability weights in the presence of linear utility. The first important difference is that utility may have a kink at the status quo, which allows for the exhibition of loss aversion. Also, we may have different probability weighting functions for gains than for losses. The central condition of our model is termed independence of common increments. The applications of our model to portfolio selection and insurance demand show that CPT with linear utility has more realistic implications than the dual theory since it implies only a weakened variant of plunging.

Rationality and dynamic consistency under risk and uncertainty

For choice with deterministic consequences, the standard rationality hypothesis is ordinality - i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann{Morgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage's sure thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behaviour in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behavior violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments

Parametric Weighting Functions

This paper provides behavioral foundations for parametric weighting functions under rankdependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by restricting the conditions to subsets of the probability interval, foundations of rank-dependent utility with parametric inverse-S shaped weighting functions are obtained. --Comonotonic independence,probability weighting function,preference foundation,rank-dependent utility

Additive utility in prospect theory

Prospect theory is currently the main descriptive theory of decision under uncertainty. It generalizes expected utility by introducing nonlinear decision weighting and loss aversion. A difficulty in the study of multiattribute utility under prospect theory is to determine when an attribute yields a gain or a loss. One possibility, adopted in the theoretical literature on multiattribute utility under prospect theory, is to assume that a decision maker determines whether the complete outcome is a gain or a loss. In this holistic evaluation, decision weighting and loss aversion are general and attribute-independent. Another possibility, more common in the empirical literature, is to assume that a decision maker has a reference point for each attribute. We give preference foundations for this attribute-specific evaluation where decision weighting and loss aversion are depending on the attributes