Stochastic Dominance and Risk Comparisons

Abstract

According to the expected utility theory, an individual should rank uncertain prospects according to the expected utilities from the prospects. If we do not know exactly the specific utility function defined on the space of outcomes, we cannot predict how the individual is going to rank the prospects. The literature on stochastic dominance started with the following problem. Suppose we know that the utility function of an individual is given by u = f(w), where w stands for the wealth of the individual. We do not know the exact form of the utility function except that it is an increasing function of w, f′ > 0. Given two lotteries L1 and L2, can we predict how this individual will rank the lotteries? In general, it is not possible to predict the ranking with such a small amount of information. However, if L1 and L2 satisfy certain conditions, we can predict the ranking. One such condition is known as the condition for first order stochastic dominance. This condition was first discussed in Quirk and Saposnik (1962) and later on generalized by Hadar and Russell (1969).