RARE EVENT ANALYSIS AND EFFICIENT SIMULATION FOR A MULTI-DIMENSIONAL RUIN PROBLEM. Issue 3 (23rd January 2017)

• Record Type: Journal Article
• Authors: Cahen, Ewan Jacov; Mandjes, Michel; Zwart, Bert
• Is Part Of: Probability in the engineering and informational sciences. Volume 31:Issue 3(2017)
• Page Start: 265
• Page End: 283
• Publication Date: 2017-01-23
• Subjects: Large deviations, -- importance sampling, -- rare-event simulation, -- ruin probability; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964816000553
• Languages: English
• ISSNs: 0269-9648

Abstract

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.