RARE EVENT ANALYSIS AND EFFICIENT SIMULATION FOR A MULTI-DIMENSIONAL RUIN PROBLEM. Issue 3 (23rd January 2017) - Cahen, Ewan Jacov; Mandjes, Michel; Zwart, Bert
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.