An algorithm for optimal stopping with path-dependent rewards based on regression and malliavin calculus

We develop a new algorithm to solve optimal stopping problems. This algorithm is particularly interesting for path-dependent problems. The originality of our method is that it does not transform the model into a Markov model. Rather, we use tools from Malliavin calculus to develop a pathwise approximation of the continuation value. We then regress the latter on a set of basis functions like in the Longstaff-Schwartz (2001) algorithm. The advantage of our scheme is that the number of basis functions required to approximate the continuation value is reduced. As a result, the overall computation time is reduced in path-dependent problems.