Non-concave utility maximisation on the positive real axis in discrete time

TL;DR

This paper addresses a discrete-time asset allocation problem with non-concave utility functions, proving the existence of optimal portfolios in incomplete markets with non-negative wealth constraints.

Contribution

It establishes the existence of optimal portfolios under non-concave utilities in incomplete markets, a novel extension in discrete-time financial modeling.

Findings

Existence of optimal portfolios proven under specified conditions

Applicable to markets with non-concave utility functions

Wealth remains non-negative throughout investment

Abstract

We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.