A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios

TL;DR

This paper proves a limit theorem for optimal trading strategies under proportional transaction costs, addressing an open question and establishing uniqueness using a dual approach.

Contribution

It introduces a limit theorem for utility maximization with transaction costs and proves the uniqueness of optimal strategies using a dual approach.

Findings

Established a limit theorem for optimal strategies

Proved the uniqueness of the optimal trading strategy

Resolved an open question in the field

Abstract

The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. The proof of the uniqueness is heavily based on the dual approach which was developed recently in [6,7,8].