Saddlepoint approximations to the probability of ruin in finite time for the compound Poisson risk process perturbed by diffusion

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Authors Riccardo Gatto, Benjamin Baumgartner
Journal/Conference Name Methodology and Computing in Applied Probability
Paper Category
Paper Abstract A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.
Date of publication 2016
Code Programming Language R

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