LQG for Portfolio Optimization

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.

Keywords: Portfolio optimization, Impact, Return predictability, LQR, LQG, Riccati, State-space

JEL Classification: C02, C32, C61, D81, G11