Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach

TL;DR

This paper uses convex duality and shadow price processes to rigorously verify the leading-order optimal trading policy and welfare effects of small transaction costs for an investor with constant absolute risk aversion trading a risky asset.

Contribution

It provides a rigorous convex duality framework to validate previous formal results on optimal trading under small transaction costs.

Findings

Verification of the leading-order optimal trading policy

Quantification of welfare impact due to transaction costs

Application of shadow price processes in convex duality approach

Abstract

We consider an investor with constant absolute risk aversion who trades a risky asset with general Ito dynamics, in the presence of small proportional transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the leading-order optimal trading policy and the associated welfare impact of transaction costs. In the present paper, we carry out a convex duality approach facilitated by the concept of shadow price processes in order to verify the main results of Kallsen and Muhle-Karbe under well-defined regularity conditions.