Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

Riccardo Gatto () and Benjamin Baumgartner ()
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Riccardo Gatto: University of Bern
Benjamin Baumgartner: University of Bern

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 1, 217-235

Abstract: 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.

Keywords: Conditional distribution; cumulant generating function; Gerber-Shiu function; Importance sampling; Laplace transform; Large deviations techniques; Monte Carlo simulation; Relative error; 60G51; 41A60; 65C05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-014-9412-9

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