A Theory of Decision-Making Under Risk as a Tradeoff between Expected Utility, Expected Utility Deviation and Expected Utility Skewness

Abstract

This paper presents a new decision theory for modelling choice under risk. The new theory is a two-parameter generalization of expected utility theory. The proposed theory assumes that a decision maker: 1) behaves as if maximizing expected utility; but 2) may experience disappointment (elation) when the utility of a lottery’s outcome falls short of (exceeds) the expected utility of the lottery; and 3) may have a preference for gambling (attraction/aversion to positively/negatively skewed lotteries). The proposed theory can rationalize the fourfold pattern of risk attitudes; the common ratio effect and the reverse thereof (in certain types of decision problems); the Allais paradox in classical common consequence problems and the reverse Allais paradox — in common consequence problems with an even split of a probability mass; violations of the betweenness axiom; switching behavior in the Samuelson’s example; violations of ordinal, upper and lower cumulative independence (which falsify rank-dependent utility and cumulative prospect theory); and preference reversals between valuations and choice. Behavioral characterization (axiomatization) of the theory is provided. In application to insurance, the theory can rationalize full insurance with an actuarially unfair premium and aversion to probabilistic insurance. In application to optimal portfolio investment, the theory can rationalize the equity premium puzzle.

Keywords: Decision Theory, Risk, Expected Utility Theory, Allais paradox, Disappointment, Equity Premium Puzzle, Insurance, fourfold pattern of risk attitudes, common ratio effect, preference reversals

JEL Classification: D01, D03, D81