Computational and Applied Mathematics seminar

Abstract: Variance reduction techniques are of crucial importance for increasing efficiency of Monte Carlo simulations. Neural stochastic differential equations (SDEs), with control variates parameterized by neural networks, are considered in order to learn approximately optimal control variates and hence reduce variance. A black-box fashion practical variance reduction tool, which does not require any lengthy pre-training and tuning, is proposed for both SDEs driven by Brownian motion and, more generally, by Lévy processes including those with infinite activity. For the latter case, optimality conditions for the variance reduction are proved. Weak approximation of SDEs governed by infinite-activity Lévy processes is also discussed. Several numerical examples from option pricing are presented. The talk is mainly based on a joint work with Piers Hinds.