Seminario - Rare Event Simulation: Least-Squares Monte Carlo Method vs Deep Learning Based Shooting Method
Giovedì 25 novembre alle ore 15:30 presso l'aula Magna, il prof. Omar Kebiri della Brandenburg University of Technology (BTU), Germany, in visita al nostro Dipartimento per il progetto EUNICE, terrà un seminario dal titolo "Rare Event Simulation: Least-Squares Monte Carlo Method vs Deep Learning Based Shooting Method".
Il seminario si svolgerà in modalità mista; si riporta di sotto il link per la riunione Teams. Tutti gli interessati, colleghi, dottorandi e studenti sono invitati a partecipare.
Abstract: When computing small probabilities associated with rare events by Monte Carlo it so happens that the variance of the estimator is of the same order as the quantity of interest. Importance sampling is a means to reduce the variance of the Monte Carlo estimator by sampling from an alternative probability distribution under which the rare event is no longer rare. Determine the optimal (i.e. zero variance) changes of measure leads to a stochastic optimal control problem. The control problem can be solved by a stochastic approximation algorithm, using the Feynman-Kac representation of the associated dynamic programming equations which leads to an FBSDE, and we discuss numerical aspects for high-dimensional problems along with simple toy examples using two methods: least-squares Monte Carlo method and deep learning based shooting method. Joint work with Carsten Hartmann, Lara Neureither, and Lorenz Richter.