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.