Rare-event Simulation Methodology for Perpetuities (with H. Lam and B. Zwart).

Summary:

The paper develops asymptotically optimal algorithms for the tail distribution of a perpetuity (in contrast to mean values, which are most commonly studied in simulation). The problem is challenging because it combines both light and heavy-tailed features (light tailed input of discount rates often yields heavy-tailed perpetuities). We show that the most natural algorithm (inspired on large deviations theorey) actually typically yields infinite variance, thereby providing an example in the spirit of Glasserman and Wang (1997) Ann. Appl. Prob. 7, 731-746 that importance sampling must be applied with care. Then, we provide a couple of algorithms that are shown to be optimal. One of them is state-dependent and based on the construction of a nice (in my view) Lyapunov inequality.

Bibtex:

@Article{BlaLamZwart2010,

author = {J. Blanchet and H. Lam and B. Zwart},

title = {Rare-event simulation methodology for perpetuities},

journal = {Pre-print},

year = {2010},

volume = {},

pages = {}

}