Optimal Trading with Signals and Stochastic Price Impact

TL;DR

This paper investigates optimal trading strategies in markets with stochastic, fast-mean reverting price impacts, using singular perturbation methods to approximate solutions and analyzing the effects of stochastic frictions through numerical experiments.

Contribution

It introduces a novel approximation approach for optimal trading under stochastic, mean-reverting price impacts using singular perturbation techniques.

Findings

Approximations are accurate to the specified order.

Stochastic trading frictions significantly influence optimal trading strategies.

Numerical experiments illustrate the impact of stochastic frictions on trading behavior.

Abstract

Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem using singular perturbation methods. We prove, by constructing sub- and super-solutions, that the approximations are accurate to the specified order. Finally, we perform some numerical experiments to illustrate the effect that stochastic trading frictions have on optimal trading.