Maximization of Non-Concave Utility Functions in Discrete-Time Financial Market Models

TL;DR

This paper explores the problem of maximizing expected terminal utility in discrete-time financial markets with possibly non-concave utility functions, establishing conditions for the existence of optimal strategies based on asymptotic elasticity.

Contribution

It introduces conditions ensuring the existence of optimal strategies for non-concave utility maximization in incomplete markets, emphasizing the role of asymptotic elasticity.

Findings

Existence of optimal strategies under specific asymptotic elasticity conditions

Conditions applicable to non-concave utility functions in discrete-time models

Extension of utility maximization theory to more general utility functions

Abstract

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility function $U$ is considered, with domain of definition $\mathbb{R}$. Simple conditions are presented which guarantee the existence of an optimal strategy for the problem. In particular, the asymptotic elasticity of $U$ plays a decisive role: existence can be shown when it is strictly greater at $-\infty$ than at $+\infty$.