Lottery valuation using the aspiration / relative utility function

Abstract

The paper presents a method for lottery valuation using the relative utility function. This function was presented by Kontek (2009) as “the aspiration function” and resembles the utility curve proposed by Markowitz (1952A). The paper discusses lotteries with discrete and continuous outcome distributions as well as lotteries with positive, negative and mixed outcomes providing analytical formulas for certainty equivalents in each case. The solution is similar to the Expected Utility Theory approach and does not use the probability weighting function – one of the key elements of Prospect Theory. Solutions to several classical behavioral problems, including the Allais paradox, are presented, demonstrating that the method can be used for valuing lotteries even in more complex cases of outcomes described by a combination of Beta distributions. The paper provides strong arguments against Prospect Theory as a model for describing human behavior and lays the foundations for Relative Utility Theory – a new theory of decision making under conditions of risk.