Optimal Selling Strategies under Regime-Switching Market Environment with Finite Expiry

This paper addresses an optimal stock liquidation problem over a finite-time horizon; to that end, we model it as an optimal stopping problem in a regime-switching market. The optimal stopping time is written as a solution to a system of Volterra type integral equations. Moreover, it reveals that when the risk-free interest rate is always lower than the return rate of the stock, it is never optimal to sell the stock early; otherwise, one should sell the stock in bear market if the stock price reaches a critical value and hold the stock in bull market until the maturity date. Finally, we present a trinomial tree method for numerical implementation. The numerical results are consistent with the theoretical findings.

Automated summary

This paper examines an optimal stock liquidation problem over a finite-time horizon, modeling it as an optimal stopping problem in a regime-switching market and providing a numerical approach to finding the optimal stopping time. The results offer insights into the optimal stock liquidation strategy under specific conditions, along with a numerical implementation approach.