Structure of optimal stopping domains for American options with knock out domains

American options give us the possibility to exercise them at any moment of time up to maturity. An optimal stopping domain for American type options is a domain that, if the underlying price process enters we should exercise the option. A knock out option is a American barrier option of knock out type, but with more general shape structure of the knock out domain. An algorithm for generating the optimal stopping domain for American type knock out options is constructed. Monte Carlo simulation is used to determine the structure of the optimal stopping domain. Results of the structural, and stability of studies are presented for different models of payoff functions and knock out domains