High-order Markov-switching portfolio selection with capital gain tax

The uncertainties of market state and returns of risky assets both affect the investors' decisions significantly. It is necessary and prudent to consider the regime-switching mechanism of market states in portfolio selection. Different from the traditional first-order Markov-switching portfolio selection studies, we consider a high-order Markov transition process of market state, which can better depict the market state changes and incorporate more market information into portfolio selection due to the financial market has the long memory property. The capital gain tax is treated as the trading cost of which the tax rate not only depends on the holding periods of risky assets but also on the trading volume. In addition, the capital gain–loss offsetting is studied explicitly where the gain–loss offsetting in the same period and capital loss carry-over effect in different periods are considered simultaneously. A high-order Markov-switching portfolio selection model (HOMSPSM) is proposed. The Monte Carlo simulation is employed to approximate the expected values and variances of the complicated random returns, and the Monte Carlo simulation based particle swarm optimization algorithm (MCPSO) is designed to obtain the optimal investment strategy. Finally, simulated and practical numerical experiments are provided to verify the effectiveness and practicability of HOMSPSM and MCPSO.