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. 217235. Springer 10.1007/s1100901494129
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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 nonperturbed risk process by BarndorffNielsen 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: 
13875841 
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/s1100901494129 
BORIS DOI: 
10.7892/boris.73010 
URI: 
https://boris.unibe.ch/id/eprint/73010 