Author:
Blanchet Jose,Liu Jingchen
Abstract
We consider the problem of efficient estimation via simulation of first passage time probabilities for a multidimensional random walk with heavy-tailed increments. In addition to being a natural generalization to the problem of computing ruin probabilities in insurance - in which the focus is the maximum of a one-dimensional random walk with negative drift - this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the process in connection to the location of the target set). We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, using techniques based on Lyapunov inequalities, we argue that our estimator is strongly efficient in the sense that the relative mean squared error of our estimator can be made arbitrarily small by increasing the number of replications, uniformly as the probability of interest approaches 0.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference15 articles.
1. State-dependent importance sampling for regularly varying random walks
2. Hult H. and Lindskog F. (2006). Heavy-tailed insurance portfolios: buffer capital and ruin probabilities. Tech. Rep. 1441, School of ORIE, Cornell University.
3. Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors;Collamore;Ann. Appl. Prob.,2002
4. Dupuis P. , Leder K. and Wang H. (2006). Notes on importance sampling for random variables with regularly varying tails. Preprint.
5. Efficient rare-event simulation for the maximum of heavy-tailed random walks
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献