Tid: 18 december 2013 kl 10.15-11.00. (observera tiden)

Föredragshållare: Yuya Suzuki

Titel: Rare-event simulation with Markov Chain Monte Carlo (Examensarbete/Master thesis)

Abstract: In this thesis we consider random sums with heavy-tailed increments. By the term random sum we mean a sum of random variables where the number of summands is also random. Our interest is to analyse the tail behaviour of random sums and to construct an efficient method to calculate quantiles. For the sake of efficiency, we simulate rare events using Markov chain Monte Carlo (MCMC) method. The asymptotic behaviour of the sum and the maximum of heavy-tailed random sums is identical. Therefore we compare the random sum and its maximum increment for various distributions to investigate from which point one can use the asymptotic approximation. Furthermore, we propose a new method to estimate quantiles and the estimator is shown to be efficient.

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