Monotonicity Of Value Function For Optimal Stopping Under Regime-Switching Market

General properties of value function for optimal stopping problem have been one of the focus in the area of financial mathematics. While researching on these issues, widely used methods are probability skills such as martingale analysis, mathematical expectation and martingale transform and so on. Recently, in the paper[1] the method of time-changing and coupling is used in the first time, providing a new way of thinking for research in this field. Based on this, we mainly prove monotonicity of value function for optimal stop-ping problem with risk factors which have different statistical characteristics. Specifical-ly, we use time-changing and coupling method, and with Girsanov theorem for measure change, promoting existing achievements to the situation with a general draft, and prove the monotonicity of value function in the stochatic volitality y. Finally, we apply mono-tonic conclusions to the American option pricing problem by making a corresponding change in the value function.