Ruin probabilities in a Markovian shot-noise environment

We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cramér–Lundberg model, namely the constant intensity of the Poisson process. Due to this structure, we can apply the theory of piecewise deterministic Markov...

Full description

Saved in:
Bibliographic Details
Published inJournal of applied probability Vol. 60; no. 2; pp. 542 - 556
Main Authors Pojer, Simon, Thonhauser, Stefan
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2023
Subjects
Asymptotic properties
Markov analysis
Markov processes
Martingales
Ordinary differential equations
Original Article
Probability
Random variables
Statistical analysis
Upper bounds
risk theory
piecewise-deterministic Markov processes (PDMP)
Ruin theory
Cox processes
60J25
91G05
60K10
Online AccessGet full text
ISSN0021-9002
1475-6072
DOI10.1017/jpr.2022.63

Cover

More Information
Summary:We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cramér–Lundberg model, namely the constant intensity of the Poisson process. Due to this structure, we can apply the theory of piecewise deterministic Markov processes on a multivariate process containing the intensity and the reserve process, which allows us to identify a family of martingales. Eventually, we use change of measure techniques to derive an upper bound for the ruin probability in this model. Exploiting a recurrent structure of the shot-noise process, even the asymptotic behaviour of the ruin probability can be determined.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2022.63