Error Rates and Improved Algorithms for Rare Event Simulation with Heavy Weibull Tails

Søren Asmussen () and Dominik Kortschak ()
Additional contact information
Søren Asmussen: Aarhus University
Dominik Kortschak: Université Lyon 1

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 2, 441-461

Abstract: Abstract Let Y 1,...,Y n be i.i.d. subexponential and S n = Y 1 + ⋯ + Y n . Asmussen and Kroese (Adv Appl Probab 38:545–558, 2006) suggested a simulation estimator for evaluating ${\mathbb P}(S_n>x)$ , combining an exchangeability argument with conditional Monte Carlo. The estimator was later shown by Hartinger and Kortschak (Bl DGVFM 30:363–377, 2009) to have vanishing relative error. For the Weibull and related cases, we calculate the exact error rate and suggest improved estimators. These improvements can be seen as control variate estimators, but are rather motivated by second order subexponential theory which is also at the core of the technical proofs.

Keywords: Complexity; Conditional Monte Carlo; Control variates; Lognormal distribution; M/G/1 queue; Pollaczeck–Khinchine formula; Rare event; Regular variation; Ruin theory; Second order subexponentiality; Subexponential distribution; Vanishing relative error; Weibull distribution; 65C05; 60G50; 62P05 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-013-9371-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9371-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-013-9371-6

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().