Title :
Rare-event simulation for a multidimensional random walk with t distributed increments
Author :
Blanchet, Jose H. ; Liu, Jingchen
Author_Institution :
Harvard Univ., Cambridge
Abstract :
We consider the problem of efficient estimation of first passage time probabilities for a multidimensional random walk with t distributed increments, via simulation. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance - in which the focus is a one dimensional random walk - this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the random walk in connection to the spatial location of the target set). We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, we argue - using techniques based on Lyapunov type inequalities - that our estimator is strongly efficient.
Keywords :
Lyapunov methods; estimation theory; importance sampling; probability; random processes; simulation; Lyapunov type inequality; distributed increment; heavy-tailed process; insurance; multidimensional random walk; probability; rare-event simulation; state-dependent importance sampling estimator; Algorithm design and analysis; Computational modeling; Insurance; Lyapunov method; Monte Carlo methods; Multidimensional systems; Probability; Statistical distributions; Tail; Upper bound;
Conference_Titel :
Simulation Conference, 2007 Winter
Conference_Location :
Washington, DC
Print_ISBN :
978-1-4244-1306-5
Electronic_ISBN :
978-1-4244-1306-5
DOI :
10.1109/WSC.2007.4419628