High-Order Regime-Switching Portfolio Selection

In this chapter, we examine a high-order transition framework for characterizing state dynamics, which offers a more accurate representation of market fluctuations by leveraging the long memory characteristics inherent in financial markets, thereby enabling the integration of richer market information into portfolio decisions. Capital gain tax is modeled as a transaction cost component, with tax rates varying according to both the duration of risky asset holdings and the magnitude of trading activity. Furthermore, we explicitly investigate capital gain-loss offset mechanisms, encompassing both intra-period offsetting and inter-period loss carryforward provisions. We introduce a high-order regime-switching model, denoted as HOMSPSM. To handle the computational complexity of random return distributions, Monte Carlo simulation techniques are utilized to estimate expected values and variances, while a hybrid approach combining Monte Carlo methods with PSO is developed to identify optimal strategies. The validity and practical utility of both HOMSPSM and MCPSO are demonstrated through comprehensive numerical studies involving both synthetic and empirical data.