Optimal trading with online parameters revisions

TL;DR

This paper develops a method for online parameter estimation and optimal control in trading robots, integrating Bayesian updating with impulse control to adapt to market impact observations.

Contribution

It introduces a novel approach combining Bayesian updating and optimal impulse control for real-time parameter adjustment in trading strategies.

Findings

Derivation of a dynamic programming equation for the problem.

Development of a convergent finite difference scheme.

Application to typical trading scenarios.

Abstract

The aim of this paper is to explain how parameters adjustments can be integrated in the design or the control of automates of trading. Typically, we are interested by the online estimation of the market impacts generated by robots or single orders, and how they/the controller should react in an optimal way to the informations generated by the observation of the realized impacts. This can be formulated as an optimal impulse control problem with unknown parameters, on which a prior is given. We explain how a mix of the classical Bayesian updating rule and of optimal control techniques allows one to derive the dynamic programming equation satisfied by the corresponding value function, from which the optimal policy can be inferred. We provide an example of convergent finite difference scheme and consider typical examples of applications.