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Description:
This paper presents a novel approach to reducing the complexity of simulation based policy iteration methods for solving optimal stopping problems. Typically, Monte Carlo construction of an improved policy gives rise to a nested simulation algorithm. In this respect our new approach uses the multilevel idea in the context of the nested simulations, where each level corresponds to a specific number of inner simulations. A thorough analysis of the convergence rates in the multilevel policy improvement algorithm is presented. A detailed complexity analysis shows that a significant reduction in computational effort can be achieved in comparison to the standard Monte Carlo based policy iteration. The performance of the multilevel method is illustrated in the case of pricing a multidimensional American derivative.