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