Discrete time optimal investment under model uncertainty

TL;DR

This paper develops a robust utility maximization framework for discrete-time markets under model uncertainty, proving the existence of optimal strategies with minimal assumptions.

Contribution

It introduces a primal method approach to establish optimal investment strategies in markets with ambiguity and general utility functions.

Findings

Existence of optimal strategies under model uncertainty

Framework accommodates utility functions with benchmarks

Assumptions align with classical market and utility theory

Abstract

We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also faces model ambiguity on her beliefs about the market, which is modeled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that we assume classical assumptions on the market and on the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also propose a general setting including utility functions with benchmark for which our assumptions are easily checked.