Portfolio Optimization in Affine Models with Markov Switching

TL;DR

This paper develops explicit solutions for optimal investment strategies in affine Markov switching models, including cases with leverage, by solving coupled PDEs and applying the affine structure, with illustrations on a Markov modulated Heston model.

Contribution

It derives explicit optimal investment strategies in affine Markov switching models with and without leverage, extending previous methods to this class of incomplete markets.

Findings

Explicit solutions for no-leverage case derived.

Separable ansatz yields solutions with leverage.

Illustrations provided for Markov modulated Heston model.

Abstract

We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this aim we apply Merton's approach, as we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains we first derive the HJB equations, which in our case correspond to a system of coupled non-linear PDEs. Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic factor. In the presence of leverage we propose a separable ansatz, which leads to explicit solutions in this case as well. General verification results are also proved. The results are illustrated for the special case of a Markov modulated Heston model.