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- Title
Uniformly Efficient Importance Sampling for the Tail Distribution of Sums of Random Variables.
- Authors
Glasserman, Paul; Juneja, Sandeep
- Abstract
Successful efficient rare-event simulation typically involves using importance sampling tailored to a specific rare event. However, in applications one may be interested in simultaneous estimation of many probabilities or even an entire distribution. In this paper, we address this issue in a simple but fundamental setting. Specifically, we consider the problem of efficient estimation of the probabilities P(Sn ≥ na) for large n, for all a lying in an interval A, where Sn denotes the sum of n independent, identically distributed light-tailed random variables. Importance sampling based on exponential twisting is known to produce asymptotically efficient estimates when A reduces to a single point. We show, however, that this procedure fails to be asymptotically efficient throughout A when A contains more than one point. We analyze the best performance that can be achieved using a discrete mixture of exponentially twisted distributions, and then present a method using a continuous mixture. We show that a continuous mixture of exponentially twisted probabilities and a discrete mixture with a sufficiently large number of components produce asymptotically efficient estimates for all a ∊ A simultaneously.
- Subjects
PROBABILITY theory; RANDOM variables; CREDIT risk; MULTIVARIATE analysis; MATHEMATICAL statistics; MATHEMATICS
- Publication
Mathematics of Operations Research, 2008, Vol 33, Issue 1, p36
- ISSN
0364-765X
- Publication type
Article
- DOI
10.1287/moor.1070.0276