Download or read book Sequential Methods for Rare Event Simulations written by Shaojie Deng and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider rare events modeled as a Markov Chain hitting a certain rare set. A sequential importance sampling with resampling (SISR) method is introduced to provide a versatile approach for computing such probabilities of rare events. The method uses resampling to track the zero-variance importance measure associated with the event of interest. A general methodology for choosing the importance measure and resampling scheme to come up with an efficient estimator of the probability of occurrence of the rare event is developed and the distinction between light-tailed and heavy-tailed problems is highlighted. Applications include classic tail probabilities for sums of independent light-tailed or heavy-tailed random variables. Markovian extensions and simultaneous simulation are also given. The heuristics and the methodology can also be applied to more complex Monte Carlo problems that arise in recent works on the dynamic portfolio credit risk model.