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, 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: |
05 Dec 2022 14:50 |
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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