Paper Info
Title
Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes
Abstract
This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Levy 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->~, where t>0 is the time horizon and x>0 is the starting point of the risk process, with y=t/x held constant and assumed either below or above a certain constant.
Year
DOI
Venue
2014
10.1016/j.amc.2014.05.077
Applied Mathematics and Computation
Keywords
Field
DocType
bounded relative error,lundberg conjugated measure,legendre-fenchel transform,logarithmic efficiency,exponential tilt,ruin due to creeping and to jump
Mathematical optimization,Importance sampling,Time horizon,Mathematical analysis,Horizon,Logarithm,Ruin theory,First-hitting-time model,Mathematics,Compound Poisson process,Bounded function
Journal
Volume
Issue
ISSN
243
1
0096-3003
Citations 
PageRank 
References 
1
0.63
2
Authors
1
Name
Order
Citations
PageRank
Riccardo Gatto1125.65