A Closer Look at Stochastic Dominance and Risk in Financial Economics

Abstract

We take a closer look at two basic ingredients in investment and actuarial sciences, namely utility and risk. We establish rigorous approximations of utility functions in order to provide general foundations for stochastic dominance rules. We systematically use Choquet integral properties to derive various desirable properties of risk measures as well as to discuss consistency of coherent risk measures with respect to stochastic dominance rules. Statistical aspects of risk estimation will be also addressed.