Optimal Trading with Linear Costs

TL;DR

This paper derives the optimal trading strategy under linear costs and position caps, showing it involves switching between maximum long and short positions based on predictor thresholds, with explicit solutions for certain predictors.

Contribution

It introduces a threshold-based optimal trading strategy with linear costs and position limits, providing explicit solutions and analyzing cost dependence.

Findings

Optimal strategy switches at predictor thresholds

Explicit threshold equations for Ornstein-Uhlenbeck predictor

Threshold relates to non-trading band in quadratic risk case

Abstract

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch between the maximum allowed long position and the maximum allowed short position, whenever the predictor exceeds a threshold value, for which we establish an exact equation. This equation can be solved explicitely in the case of a discrete Ornstein-Uhlenbeck predictor. We discuss in detail the dependence of this threshold value on the transaction costs. Finally, we establish a strong connection between our problem and the case of a quadratic risk penalty, where our threshold becomes the size of the optimal non-trading band.