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

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 $+\infty$.