Risk-sensitive decision-making under risk constraints with coherent risk measures

Abstract

Risk-sensitive decision-making with constraints of coherent risk measures is discussed. Risk-sensitive expected rewards under utility functions are approximated by weighted average value-at-risks, and risk constraints are described by coherent risk measures. In this paper, coherent risk measures are represented as weighted average value-at-risks with the best risk spectrum derived from decision-maker’s risk averse utility, and the risk spectrum can inherit the risk averse property of the decision-maker’s utility as weighting. To find feasible regions, first, a dynamic risk-minimizing problem is discussed by mathematical programming. Next, a risk-sensitive reward maximization problem under the feasible coherent risk constraints is demonstrated. A few numerical examples are given to understand the obtained results.