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Rare event simulation for the ruin problem with investments via importance sampling and duality

Collamore, JF; Vidyashankar, AN (Copenhagen; George Mason)
Monday 21 June 2010, 10:00-10:25

Seminar Room 1, Newton Institute


We develop an efficient importance sampling algorithm for a Cramér-Lundberg insurance model with stochastic investments. Our approach utilizes the duality between this process and an extended GARCH(1,1) financial process. Using this duality and the regenerative structure of the GARCH(1,1) financial process, we introduce a novel large deviation change of measure idea to compute the probability of ruin for the insurance process. Finally, we examine state-dependent importance sampling in the context of this problem and comment on statistical aspects of our algorithm.


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