Optimal Expected Utility Risk Measures

Abstract

This paper introduces optimal expected utility (OEU) risk measures, investigates their main properties and puts them in perspective to alternative risk measures and notions of certainty equivalents. Taking the investor’s point of view, OEU maximizes the sum of capital available today and the certainty equivalent of capital in the future. To the best of our knowledge, OEU is the only existing utility-based risk measure that is (non-trivial and) coherent if the utility function u has constant relative risk aversion. We present several different risk measures that can be derived with special choices of u and illustrate that OEU is more sensitive than value at risk and average value at risk with respect to changes of the probability of a financial loss.

Keywords: risk measure, certainty equivalent, utility maximization