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Rare event simulation involving heavy tailed random variables finds wide application in communications, insurance as well as finance where accurate measurement of small probabilities is often critically important. This area has generated considerable interest amongst applied probabilists for the past fifteen years. In this talk, we develop state-independent importance sampling based efficient simulation techniques for two practically important and basic rare event probabilities associated with a random walk {S_n} with regularly varying heavy-tailed increments: namely, the level crossing probabilities when the increments of {S_n} have a negative mean, and the the large deviation probabilities P(S_n > b) as both n and b increase to infinity for the zero mean random walk. Exponential twisting based state-independent methods, which are effective in efficiently estimating these probabilities for light-tailed increments are not applicable when these are heavy-tailed. To address the latter case, more complex state-dependent efficient simulation algorithms have been developed in the literature over the last few years. We propose that by suitably decomposing these rare event probabilities into a dominant and further residual components, simpler state-independent importance sampling algorithms can be devised for each component resulting in composite unbiased estimators with a desirable vanishing relative error property. When the increments have infinite variance, there is an added complexity in estimating level crossing probabilities as even the well known zero variance measures have an infinite expected termination time. We adapt our algorithms so that this expectation is finite while the estimators remain strongly efficient. Numerically, the proposed estimators perform at least as well, and sometimes substantially better than the existing state-dependent estimators in the literature

rare_event_simulation_of_heavy_tailed_random_walks_a_new_approach.txt · Last modified: 2016/09/01 19:15 (external edit)