Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156654 | Stochastic Processes and their Applications | 2012 | 32 Pages |
Abstract
We consider perpetuities of the form D=B1exp(Y1)+B2exp(Y1+Y2)+â¯, where the Yj's and Bj's might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Yj's satisfy the so-called Cramér condition with associated root θââ(0,â) and that the tails of the Bj's are appropriately behaved so that D is regularly varying with index θâ. We illustrate by means of an example that the natural state-independent importance sampling estimator obtained by exponentially tilting the Yj's according to θâ fails to provide an efficient estimator (in the sense of appropriately controlling the relative mean squared error as the tail probability of interest gets smaller). Then, we construct estimators based on state-dependent importance sampling that are rigorously shown to be efficient.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jose Blanchet, Henry Lam, Bert Zwart,