Optimal Stopping with Model Uncertainty and Pricing the American Option

In order to formulate the skewness, excess kurtosis of the stock price and model uncertainty, this paper concerns a g-martingale characterization of value process of American put-option in a jump-diffusion model; Furthermore, we give a new free boundary problem tool for pricing the American put-option. And we can compute the size of model uncertainty by the market data. Our methods lead to an effective investment strategy against the stock price behaviour and model uncertainty.