Extended Weak Convergence and Utility Maximization with Proportional Transaction Costs

TL;DR

This paper investigates utility maximization in financial markets with proportional transaction costs, proving convergence of optimization problems and strategies under extended weak convergence assumptions.

Contribution

It introduces a limit theorem for optimal trading strategies and applies extended weak convergence theory to utility maximization with transaction costs.

Findings

Convergence of utility maximization problems established

Limit theorem for optimal trading strategies proven

Application of extended weak convergence theory in finance

Abstract

In this paper we study utility maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding utility maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in [1] and the Meyer--Zheng topology introduced in [24].