Valuing American options by simulation: A BSDEs approach

We provide probabilistic proofs of convergence of several easy to implement schemes for computing the value function of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. The proofs are based on representations of the value function by means of solutions of some backward stochastic differential equations. Despite the probabilistic nature of the proofs the numerical schemes are nevertheless deterministic. Simulation results are also presented.