Quantization based recursive importance sampling

Abstract

We propose an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We consider an algorithm which combines (vector and functional) optimal quantization with Newton-Raphson zero search procedure. Our approach can be seen as a robust and automatic deterministic counterpart of recursive importance sampling (by translation of the mean) by means of stochastic approximation algorithm which may require tuning of the step sequence and a good knowledge of the payoff function in practice. Moreover, unlike recursive importance sampling procedures, the proposed methodology does not rely on simulations so it is quite fast, generic and can come along on the top of Monte Carlo simulations.