Claremont Center for the Mathematical Sciences

We propose a recursive scheme to calculate backward the values of
conditional expectations of functions of path values of Brownian motion.
This scheme is based on the Clark-Ocone formula in discrete time. We
construct an algorithm based on our scheme to efficiently calculate the
price of American options on securities with path-dependent payoffs. Our
algorithm can be combined with regression-based Monte Carlo methods,
like the Tsitsiklis-Van Roy algorithm. In this case, our algorithm
remedies the decrease of performance experienced by regression-based
methods when the number of basis functions, or regressands, needs to be
quite large, because of path-dependence.
In the future we plan to apply our recursive scheme to find asymptotic
solutions to non-Markovian stochastic control problems. This is joint
work with Hedley Morris.