The Increase Convex Order and the Tradeoff of Size for Risk

Abstract

One random variable is larger than another in the increasing convex order if that random variable is preferred or indifferent to the other by all decision makers with increasing and convex utility functions. Decision makers in this set prefer larger random variables and are risk loving. When a decision maker whose utility function is increasing and concave is indifferent between such a pair of random variables, a tradeoff of size for risk is revealed, and this information can be used to make comparative static predictions concerning the choices of others. For random variables ranked by the increasing convex order, the choices of all those who are strongly more (or less) risk averse can be predicted. Thus, the increasing convex order, together with Ross’s (1981) definition of strongly more risk averse, can provide additional comparative static findings in a variety of decision problems. The analysis here discusses the decision to self-protect, and several others.