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Spectrally negative Lévy processes with applications in risk theory
- Source :
- Advances in Applied Probability. 33:281-291
- Publication Year :
- 2001
- Publisher :
- Cambridge University Press (CUP), 2001.
-
Abstract
- In this paper, results on spectrally negative Lévy processes are used to study the ruin probability under some risk processes. These processes include the compound Poisson process and the gamma process, both perturbed by diffusion. In addition, the first time the risk process hits a given level is also studied. In the case of classical risk process, the joint distribution of the ruin time and the first recovery time is obtained. Some results in this paper have appeared before (e.g., Dufresne and Gerber (1991), Gerber (1990), dos Reis (1993)). We revisit them from the Lévy process theory's point of view and in a unified and simple way.
- Subjects :
- Statistics and Probability
050208 finance
Subordinator
Applied Mathematics
Mathematical analysis
Gamma process
05 social sciences
Lévy process
01 natural sciences
010104 statistics & probability
Joint probability distribution
Simple (abstract algebra)
Compound Poisson process
0502 economics and business
Applied mathematics
First-hitting-time model
0101 mathematics
Variance gamma process
Mathematics
Subjects
Details
- ISSN :
- 14756064 and 00018678
- Volume :
- 33
- Database :
- OpenAIRE
- Journal :
- Advances in Applied Probability
- Accession number :
- edsair.doi.dedup.....1abfb20c315413eefdf2f03d598ead70