Dynamic risk-sensitive fuzzy asset management with coherent risk measures derived from decision maker’s utility

Abstract

A dynamic risk-sensitive portfolio optimization problem under risk constraints is discussed by the use of coherent risk measures and fuzzy random variables. Risk-sensitive expected rewards under utility functions are approximated by weighted average value-at-risks, and risk constraints are described by coherent risk measures. The 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. By perception-based extension, the risk-sensitive estimation and coherent risk measures are applied to fuzzy random variables. To find feasible regions of risk constraints, a one-step risk-minimizing problem is investigated by mathematical programming. Next, dynamic risk-sensitive total reward maximization under the feasible coherent risk constraints is discussed by dynamic programming. A few numerical examples are investigated to explain the significance of the obtained results. The proposed method is extremely effective for high-speed portfolio trading.