Efficient simulation of tail probabilities of sums of dependent random variables

Blanchet, Jose H. and Rojas-Nandayapa, Leonardo (2011) Efficient simulation of tail probabilities of sums of dependent random variables. Journal of Applied Probability, 48A 147-164. doi:10.1239/jap/1318940462

Author Blanchet, Jose H.
Rojas-Nandayapa, Leonardo
Title Efficient simulation of tail probabilities of sums of dependent random variables
Journal name Journal of Applied Probability   Check publisher's open access policy
ISSN 0021-9002
ISBN 9780902016088
Publication date 2011-08
Sub-type Article (original research)
DOI 10.1239/jap/1318940462
Volume 48A
Start page 147
End page 164
Total pages 18
Place of publication S Yorks, United Kingdom
Publisher Applied Probability Trust
Collection year 2012
Language eng
Formatted abstract
We study asymptotically optimal simulation algorithms for approximating the tail probability of P(eX1+⋯+ eXd>u) as u→∞. The first algorithm proposed is based on conditional Monte Carlo and assumes that (X1,…,Xd) has an elliptical distribution with very mild assumptions on the radial component. This algorithm is applicable to a large class of models in finance, as we demonstrate with examples. In addition, we propose an importance sampling algorithm for an arbitrary dependence structure that is shown to be asymptotically optimal under mild assumptions on the marginal distributions and, basically, that we can simulate efficiently (X1,…,Xd|Xj >b) for large b. Extensions that allow us to handle portfolios of financial options are also discussed.
Keyword Rare-event simulation
Heavy-tailed dis-tributions
Log-elliptical distributions
Tail probabilities
Variance reduction
Importance sampling
Conditional Monte Carlo
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Special Volume: New frontiers in Applied probability. A Festschrift for Soren Asmussen published on the occasion of his 65th birthday, celebrates his lifelong achievements in applied probability. Edited by P. Glynn, T. Mikosch and T. Rolski. Part 4. Simulation

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
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Created: Fri, 14 Oct 2011, 15:44:21 EST by Dr Leonardo Rojas-nandayapa on behalf of Mathematics