Blanchet J, Liu J. Efficient importance sampling in ruin problems for multidimensional regularly varying random walks. Journal of Applied Probability. 2010;47(2):301-322. doi:10.1239/jap/1276784893
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 …
Authors
Jose Blanchet, Jingchen Liu
Publication date
2010/6
Journal
Journal of Applied Probability
Volume
47
Issue
2
Pages
301-322
Publisher
Cambridge University Press
