Hybrid stock-investment models and asset allocation

Abstract

We consider a class of hybrid stock-investment models involving geometric Brownian motions modulated by a continuous-time Markov chain. Our objective is to find nearly optimal asset allocation strategies to maximize the expected returns. The use of the Markov chain stems from the consideration of capturing the market trends as well as various economic factors. To incorporate various economic factors into consideration, the underlying Markov chain inevitably has a large state space. To reduce the complexity, we suggest a hierarchical approach resulting in singularly perturbed switching diffusion processes. By aggregating the states of the Markov chains in each weakly irreducible class into a single state, we obtain a limit switching diffusion process. Using such asymptotic properties, we then obtain nearly optimal asset allocation policies.