An importance sampling algorithm for estimating extremes of perpetuity sequences

Jeffrey F. Collamore

doi:10.1063/1.4756571

An importance sampling algorithm for estimating extremes of perpetuity sequences

Institut for Matematiske Fag

Abstract

In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence. This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described which is efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. The main idea of the algorithm is to use a “dual” change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval. The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion, together with elements of Markov chain theory.

Originalsprog	Engelsk
Titel	AIP Conference Proceedings
Antal sider	4
Vol/bind	1479
Forlag	American Institute of Physics
Publikationsdato	2012
Sider	1966-1969
ISBN (Trykt)	8-0-7354-1091-6
DOI	https://doi.org/10.1063/1.4756571
Status	Udgivet - 2012

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10.1063/1.4756571

http://proceedings.aip.org/

Citationsformater

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N2 - In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence. This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described which is efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. The main idea of the algorithm is to use a "dual" change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval. The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion, together with elements of Markov chain theory.

AB - In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence. This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described which is efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. The main idea of the algorithm is to use a "dual" change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval. The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion, together with elements of Markov chain theory.

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DO - 10.1063/1.4756571

M3 - Article in proceedings

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VL - 1479

SP - 1966

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BT - AIP Conference Proceedings

PB - American Institute of Physics

ER -

An importance sampling algorithm for estimating extremes of perpetuity sequences

Abstract

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