Dynamic trading with Markov liquidity switching

Abstract

In this paper, we solve a continuous-time portfolio choice problem of an investor under a Markov jump linear system that effectively captures stochasticity in asset returns, price impacts, and market resilience. Specifically, the investor chooses his portfolio to maximize the expected excess returns netting risks and trading costs due to the price impacts in a Markov switching market. We show that the value function and the optimal feedback trading strategy can be expressed in terms of the solution of a coupled matrix Riccati differential system. The presence of the market resilience and the Markov switching results in the coupled Riccati system being non-canonical. We manage to establish a set of transparent sufficient conditions to ensure the well-posedness of the coupled system. Our numerical results indicate that the investor trades more (less) aggressively in a liquidity regime where the temporary price impact is low (high) and permanent price impact is high (low) with low (high) market resilience.