Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

Gatto, Riccardo (2014). Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes. Applied mathematics and computation, 243, pp. 91-104. Elsevier 10.1016/j.amc.2014.05.077

[img] Text
GattoImportance.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (526kB) | Request a copy
[img]
Preview
Text
Gatto Importance Sampling.pdf - Accepted Version
Available under License Publisher holds Copyright.

Download (321kB) | Preview

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:

0096-3003

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

Actions (login required)

Edit item Edit item
Provide Feedback