Optimal Stopping Time and Pricing of Exotic Options

【摘要】：The purpose of this paper is to develop a general framework to analyze the optimal stopping problem relevant to the exotic option.In general,the pricing of the American style path-dependent option is equivalent to solving an optimal stop-ping problem.We turn the optimal stopping problem relevant to the American style path-dependent option into a constrained nonlinear programming in a infinite dimensional Banach space,and prove that the existence of the optimal stopping time of the optimal stopping problem relevant to a class exotic option(Asian option,Lookback option).