Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures

TL;DR

This paper introduces a weighted entropic risk measure (WERM) for optimal investment, providing explicit solutions and an iterative method for utility maximization and risk minimization under this measure.

Contribution

It characterizes the solutions to investment problems using WERM, a risk measure consistent with stochastic dominance and additive for independent sums, and offers an explicit solution framework.

Findings

Explicit solutions for utility maximization and risk minimization problems.

An iterative method for computing solutions is developed.

WERM is shown to be consistent with second-order stochastic dominance.

Abstract

A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is same to a problem of maximizing a weighted average of constant-absolute-risk-aversion (CARA) certainty equivalents. The solutions of all the optimization problems are explicitly characterized and an iterative method of the solutions is provided.