Mike Ludkovski (University of California at Santa Barbara)

We propose a new approach to solve optimal stopping problems via simulation. We reinterpet the Longstaff-Schwartz strategy of approximating the stopping regions as a statistical contour-finding problem with noisy observations. Accordingly, a key new objective that we pursue is efficient design of the stochastic grids formed by the simulated sample paths of the underlying state process. To this end, we introduce sequential design schemes that adaptively place new grid points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the state space partitions. To illustrate, we compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options. Numerical experiments show that an order of magnitude savings in terms of total grid size can be achieved. Time permitting, we will also discuss extension to optimal switching problems, such as gas storage valuation.