Optimal importance sampling for simulation of L?vy processes

This paper provides an efficient algorithm using Newton´s method under sample average approximation (SAA) to solve the parametric optimization problem associated with the optimal importance sampling change of measure in simulating Lévy processes. Numerical experiments on variance gamma (VG), geometric Brownian motion (GBM), and normal inverse Gaussian (NIG) examples illustrate the computational advantages of the SAA-Newton algorithm over stochastic approximation (SA) based algorithms.