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

Gatto, Riccardo; Baumgartner, Benjamin (2016). Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion. Methodology and Computing in Applied Probability, 18(1), pp. 217-235. Springer 10.1007/s11009-014-9412-9

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Gatto, Riccardo and Baumgartner, Benjamin

Subjects:

500 Science > 510 Mathematics

ISSN:

1387-5841

Publisher:

Springer

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

19 Nov 2015 09:51

Last Modified:

17 Feb 2016 22:45

Publisher DOI:

10.1007/s11009-014-9412-9

BORIS DOI:

10.7892/boris.73010

URI:

https://boris.unibe.ch/id/eprint/73010

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