Gatto, Riccardo (2014). Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes. Applied mathematics and computation, 243, pp. 91104. Elsevier 10.1016/j.amc.2014.05.077
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This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.
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 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
00963003 
Publisher: 
Elsevier 
Language: 
English 
Submitter: 
Lutz Dümbgen 
Date Deposited: 
19 Dec 2014 15:28 
Last Modified: 
14 Sep 2017 18:16 
Publisher DOI: 
10.1016/j.amc.2014.05.077 
Uncontrolled Keywords: 
Bounded relative error, Exponential tilt, Legendre–Fenchel transform, Logarithmic efficiency, Lundberg conjugated measure, Ruin due to creeping and to jump 
BORIS DOI: 
10.7892/boris.61149 
URI: 
https://boris.unibe.ch/id/eprint/61149 