Optimal investment with bounded above utilities in discrete time markets

TL;DR

This paper proves the existence of optimal investment strategies in discrete-time markets for investors with bounded above utility functions, including those with cumulative prospect theory preferences, under certain conditions.

Contribution

It establishes the existence of optimal strategies for investors with bounded utility functions in discrete markets, extending to cumulative prospect theory preferences.

Findings

Optimal strategies exist for bounded utility investors.

Results apply to cumulative prospect theory preferences.

Market assumptions include no arbitrage and frictionless trading.

Abstract

We consider an arbitrage-free, discrete time and frictionless market. We prove that an investor maximising the expected utility of her terminal wealth can always find an optimal investment strategy provided that her dissatisfaction of infinite losses is infinite and her utility function is non-decreasing, continuous and bounded above. The same result is shown for cumulative prospect theory preferences, under additional assumptions.