Discrete time optimal investment under model uncertainty

Abstract

We study a robust utility maximisation 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 in her beliefs about the market, which is modelled 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 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 benchmarks for which our assumptions can be easily checked.