Asymptotic methods for transaction costs

TL;DR

This paper introduces a general approximation approach for optimal trading strategies in markets with transaction costs, balancing trading frequency and size for practical implementation.

Contribution

It presents a polynomial approximation method for residual value functions and demonstrates its application across various trading problems.

Findings

Effective approximation of optimal strategies with discrete trades.

Trade-off analysis between trading frequency and trade size.

Strategies closely match continuous optimal strategies in practice.

Abstract

We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems from optimally tracking benchmarks, hedging the Log contract, to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.