Utility maximization with proportional transaction costs under model uncertainty

TL;DR

This paper develops a framework for utility maximization in discrete-time financial markets with proportional transaction costs under model uncertainty, using randomization techniques and dynamic programming to establish optimal strategies and duality results.

Contribution

It introduces a novel dynamic programming approach and extends duality theory to markets with transaction costs under model uncertainty, generalizing previous results.

Findings

Existence of optimal trading strategies proven.

Duality theorem established in the presence of transaction costs.

Analysis of utility indifference prices in a robust setting.

Abstract

We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization techniques recently developed in \cite{BDT17} allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in \cite{bartl2016exponential}, we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in \cite{bartl2016exponential} to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.