Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors
type: Item
instance of: scholarly article
title: Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors
zbMATH Open document ID: 1021.65003
author: Jeffrey F. Collamore
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: Let \(\{S_n\}\) be a sequence of \(\mathbb{R}^n\)-valued random variables and let \(A\subset\mathbb{R}^n\) be open. Consider the hitting probability of a region \(A/\varepsilon: \{x/\varepsilon: x\in A\}\), by \(\{S_n\}\) as \(\varepsilon\to 0\). It is assumed that the mean drift of \(\{S_n\}\) is directed away from \(A\) so that this probability tends to zero as \(\varepsilon\to 0\). The aim of this paper is to use importance sampling for simulating it. For any fixed \(\varepsilon\), an efficient estimate is obtained which has certain optimality properties as \(\varepsilon\to 0\).
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1906197
zbMATH Keywords: multidimensional ruin problem
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: rare event simulation
zbMATH Keywords: hitting probabilities
zbMATH Keywords: large deviations
zbMATH Keywords: importance sampling
reviewed by: Radu Theodorescu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1015961169
OpenAlex ID: W2024309638
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DOI: 10.1214/AOAP/1015961169
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description: scientific article; zbMATH DE number 1906197