Hidden-Markov-Switching Portfolio Selection

This chapter develops a framework that incorporates capital gain tax into portfolio decision-making to incentivize prolonged investment horizons, where the applicable tax rate decreases as the holding duration extends. Concurrently, we integrate the market state transitions into the realm of fuzzy portfolio optimization, leveraging fuzzy random variables for capturing uncertainty in risky asset returns within a Markov-regime switching environment. We then introduce an adjusted L-R fuzzy number and conduct a rigorous investigation into its mathematical characteristics. Building upon these foundations, we formulate a bi-objective mean-variance optimization framework that addresses return maximization and risk minimization concerns. To navigate the identification of the portfolio efficient frontier under Pareto optimality criteria, we devise a time-varying numerical integral-based particle swarm optimization methodology (TVNIPSO). An extensive series of numerical experiments are subsequently demonstrated in the end.