LQG for portfolio optimization

TL;DR

This paper presents a Linear-Quadratic-Gaussian (LQG) framework for solving complex dynamic portfolio optimization problems involving market predictability, price impact, and partial observability, providing analytical solutions and practical insights.

Contribution

It introduces a novel LQG-based approach for portfolio optimization under realistic market conditions, linking optimal control to a non-arbitrage criterion and offering analytical tools for solution interpretability.

Findings

Derived the optimal control policy within the LQG framework.

Linked the existence of the optimal controller to a non-arbitrage condition.

Demonstrated the method on a synthetic portfolio problem.

Abstract

We introduce a generic solver for dynamic portfolio allocation problems when the market exhibits return predictability, price impact and partial observability. We assume that the price modeling can be encoded into a linear state-space and we demonstrate how the problem then falls into the LQG framework. We derive the optimal control policy and introduce analytical tools that preserve the intelligibility of the solution. Furthermore, we link the existence and uniqueness of the optimal controller to a dynamical non-arbitrage criterion. Finally, we illustrate our method using a synthetic portfolio allocation problem.