Robust Utility Maximization in Discrete-Time Markets with Friction

TL;DR

This paper establishes the existence of utility maximizers in various discrete-time financial market models, including those with frictions like transaction costs and market impact, under a robust stochastic optimization framework.

Contribution

It introduces a lineality-type condition ensuring the existence of maximizers in robust utility maximization problems, extending to markets with various frictions.

Findings

Existence of maximizers under no-arbitrage conditions.

Applicability to markets with proportional transaction costs.

Extension to models with convex costs like market impact.

Abstract

We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of an utility maximizer in the frictionless market model, markets with proportional transaction costs and also more general convex costs, like in the case of market impact.