Conergence of Monte Carlo algorithms for pricing American options
In this paper we study the convergence of the Longstaff-Schwartz algorithm for the valuation of American options. Our approach is based on empirical risk minimization initiated by Vapnik and Chervonenkis in the early 1970’s and empirical processes techniques. This allows us to prove convergence, derive error estimates and a Central Limit Theorem for the sample estimators. It also opens up a variety of extensions and generalizations.