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Let (Xn : n ≥ 0) be a sequence of i.i.d. r.v.'s with negative mean. Set S0 = 0 and define Sn = X1 + · · · + Xn. We propose an importance sampling algorithm to estimate the tail of M = max{Sn : n ≥ 0} that is strongly efficient for both light and heavy-tailed increment distributions. Moreover, in the case of heavy-tailed increments and under additional(More)
Let (<i>X<inf>n</inf>: n</i> &#8805; 0) be a sequence of iid rv's with mean zero and finite variance. We describe an efficient state-dependent importance sampling algorithm for estimating the tail of <i>S<inf>n</inf></i> = <i>X</i><inf>1</inf> + &#8230; + <i>X<inf>n</inf></i> in a large deviations framework as <i>n</i> &nearr; &#8734;. Our algorithm can be(More)
The asymptotic robustness of estimators as a function of a rarity parameter, in the context of rare-event simulation, is often qualified by properties such as bounded relative error (BRE) and logarithmic efficiency (LE), also called asymptotic optimality. However, these properties do not suffice to ensure that moments of order higher than one are well(More)
We develop a strongly efficient rare-event simulation algorithm for computing the tail of the steady-state waiting time in a single server queue with regularly varying service times. Our algorithm is based on a state-dependent importance sampling strategy that is constructed so as to be straightforward to implement. The construction of the algorithm and its(More)
Consider a sequence (X k : k ≥ 0) of regularly varying independent and identically distributed random variables with mean 0 and finite variance. We develop efficient rare-event simulation methodology associated with large deviation probabilities for the random walk (S n : n ≥ 0). Our techniques are illustrated by examples, including large deviations for the(More)
We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be efficient as the tail probability of interest decreases to zero.(More)
We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as &#x03B1; = g(E (X)), where E (X) denotes the expectation of a (possibly multidimensional) random variable X, and g(&#x00B7;) is a given deterministic function. Our estimators possess finite work-normalized variance under mild regularity(More)
Given a marked renewal point process (assuming that the marks are i.i.d.) we say that an unbounded region is stable if it contains finitely many points of the point process with probability one. In this paper we provide algorithms that allow to sample these finitely many points efficiently. We explain how exact simulation of the steady-state measure valued(More)