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Consider the problem of estimating the small probability that the maximum of a random walk exceeds a large threshold, when the process has a negative drift and the underlying random variables may have heavy tailed distributions, that is, their tail distribution decays at a subexponential rate. We consider one class of such problems that has applications in… (More)
We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon and the expected excess loss given that large losses are incurred during this horizon.… (More)
We consider the problem of optimal allocation of computing budget to maximize the probability of correct selection in the ordinal optimization setting. This problem has been studied in the literature in an approximate mathematical framework under the assumption that the underlying random variables have a Gaussian distribution. We use the large deviations… (More)
We consider the eecient estimation, via simulation, of very low buuer overrow probabilities in certain acyclic ATM queueing networks. We apply the theory of eeective bandwidths and Markov additive processes to derive an asymptotically optimal simulation scheme for estimating such probabilities for a single queue with multiple independent sources, each of… (More)
In this introductory tutorial we discuss the problem of pricing financial derivatives, the key application of Monte Carlo in finance. We review the mathematics that uses no-arbitrage principle to price derivatives and expresses derivatives price as an expectation under the equivalent martingale measure. In the presentation at the conference we will also… (More)
Successful efficient rare-event simulation typically involves using importance sampling tailored to a specific rare event. However, in applications one may be interested in simultaneous estimation of many probabilities or even an entire distribution. In this paper, we address this issue in a simple but fundamental setting. Specifically, we consider the… (More)