On utility maximization with derivatives under model uncertainty

TL;DR

This paper develops a robust utility maximization framework involving derivatives and stocks under model uncertainty, establishing duality and existence of optimal strategies without assuming a fixed probability model.

Contribution

It introduces a duality theory and proves the existence of optimal strategies in a model uncertainty setting with non-dominated probability measures.

Findings

Established duality results for utility maximization under model uncertainty

Proved the existence of optimal strategies in a non-dominated model setting

Extended the theory to convex, weakly compact sets of probability measures

Abstract

We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not necessarily dominated by a fixed probability measure. By assuming that the set of physical probability measures is convex and weakly compact, we obtain the duality result and the existence of an optimizer.