  In this work, we propose a new policy iteration algorithm for pricing
Bermudan options when the payoff process cannot be written as a function of a
lifted Markov process. Our approach is based on a modification of the
well-known Longstaff Schwartz algorithm, in which we basically replace the
standard least square regression by a Wiener chaos expansion. Not only does it
allow us to deal with a non Markovian setting, but it also breaks the
bottleneck induced by the least square regression as the coefficients of the
chaos expansion are given by scalar products on the L^2 space and can therefore
be approximated by independent Monte Carlo computations. This key feature
enables us to provide an embarrassingly parallel algorithm.
