Dynamic asset allocation with multiple regime‐switching markets

This paper considers dynamic asset allocation problem with dual or multiple regime‐switching markets, that is, portfolio optimization of an investor who receives income from a cyclical or regime‐switching labour market while invests her wealth under a cyclical or regime‐switching financial market. For this purpose, we set up a flexible and tractable optimal control framework for dual or multiple Markov‐modulated stochastic system, in which Markov chains governing these regime switching are not identical as assumed in the existing literature. Based on combining two separate Markov chains into a new synthetic Markov chain in continuous time context, we state the corresponding Hamilton‐Jacobi‐Bellman equations and derive explicit solutions and value functions under some reasonable specifications. Furthermore, we lay out a numerical exercise and illustrations for optimal asset allocation or portfolio decisions under cyclical movements of both financial and labour markets.