Multiperiod distributionally robust portfolio selection with regime-switching under CVaR risk measures

Optimal investment strategy selection has become a primary research focus in investment science and operations research. Key challenges in this field include identifying an appropriate risk measure to capture potential extreme losses, accurately modeling the impact of market volatility on investment decisions, and effectively balancing returns and risks. To handle uncertainty in return distributions, robust portfolio optimization is a more recent approach. In this study, we employ robust Conditional Value-at-Risk (CVaR) as the risk measure and propose a multi-stage robust portfolio selection model incorporating both risk-free and risky assets under a known first and second moment uncertainty set. By integrating a regime-switching framework, we derive an analytical optimal investment strategy using dynamic programming (DP) techniques. Our numerical analysis demonstrates that the optimal strategy determined by dynamic programming adjusts dynamically at each stage in response to regime switches.