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RARE EVENT ANALYSIS AND EFFICIENT SIMULATION FOR A MULTI-DIMENSIONAL RUIN PROBLEM

Published online by Cambridge University Press:  23 January 2017

Ewan Jacov Cahen ,
Michel Mandjes  and
Bert Zwart
Ewan Jacov Cahen
Affiliation:
CWI, Amsterdam, the Netherlands, E-mail: [email protected]
Michel Mandjes
Affiliation:
CWI, Amsterdam, the Netherlands, University of Amsterdam, Amsterdam, the Netherlands E-mail: [email protected]
Bert Zwart
Affiliation:
CWI, Amsterdam, the Netherlands Eindhoven University of Technology, Eindhoven, the Netherlands E-mail: [email protected]
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Abstract

This paper focuses on the evaluation of the probability that both components of a bivariate stochastic process ever simultaneously exceed some large level; a leading example is that of two Markov fluid queues driven by the same background process ever reaching the set (u, ∞)×(u, ∞), for u>0. Exact analysis being prohibitive, we resort to asymptotic techniques and efficient simulation, focusing on large values of u. The first contribution concerns various expressions for the decay rate of the probability of interest, which are valid under Gärtner–Ellis-type conditions. The second contribution is an importance-sampling-based rare-event simulation technique for the bivariate Markov modulated fluid model, which is capable of asymptotically efficiently estimating the probability of interest; the efficiency of this procedure is assessed in a series of numerical experiments.

Keywords

Large deviationsimportance samplingrare-event simulationruin probability
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 3 , July 2017 , pp. 265 - 283
Copyright
Copyright © Cambridge University Press 2017 

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