Duality Theory for Exponential Utility--Based Hedging in the Almgren--Chriss Model

TL;DR

This paper develops a duality framework for exponential utility maximization with quadratic transaction costs and applies it to derive explicit optimal hedging strategies for quadratic payoffs in the Bachelier model.

Contribution

It introduces a duality result for utility maximization under quadratic costs and provides explicit hedging strategies for quadratic payoffs in a specific model.

Findings

Explicit optimal trading strategies for quadratic payoffs.

Duality framework for utility maximization with transaction costs.

Application to the Bachelier model.

Abstract

In this paper, we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the duality, we treat utility-based hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute explicitly the optimal trading strategy.