Abstract

In this talk we consider the problem of finding unbiased variance reducing Monte Carlo estimators. An optimal estimator is characterized by a minimization problem. Our novel approach to solve this problem is based on majorization/minimization algorithms (MM-algorithms). We present a general global convergence result for this type of algorithm and construct a specific MM-algorithm for the minimization problem associated with variance reducing Monte Carlo estimators. In general, it is not possible to evaluate the objective function. Therefore, we construct large sample approximations of the objective function and associate minimization problems with these approximations. The minimization problems determine M-estimators which we use to approximate the minimum point of the original minimization problem. We discuss consistency and asymptotic normality of these M-esimators. Furthermore, we modify the MM-algorithm of the original minimization problem to obtain a MM-algorithm for calculating approximations to the M-estimators. These are approximations to optimal unbiased variance reducing Monte Carlo estimators. We present some numerical experiments in the context of derivatives pricing which show that computing these optimal estimators by an MM-algorithm is efficient.

You may download the slides here.

Thursday Nov 17 2005 6:00 p.m., HfB Room 5