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References (7)
-
S.G. Mikhlin (1957)
Integral equations -
S. Asmussen (2000)
Ruin probabilities -
S. Asmussen, Hanne Nielsen (1995)
Ruin probabilities via local adjustment coefficientsJournal of Applied Probability, 32
-
Mark Davis (1995)
Markov Models and OptimizationTechnometrics, 37
-
A. Dassios, P. Embrechts (1989)
Martingales and insurance risk, 5
-
Guojing Wang, Chunsheng Zhang, R. Wu (2003)
Ruin Theory for the Risk Process Described by PDMPsActa Mathematicae Applicatae Sinica, 19
-
Mark Davis (1984)
Piecewise‐Deterministic Markov Processes: A General Class of Non‐Diffusion Stochastic ModelsJournal of the royal statistical society series b-methodological, 46
- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by Springer-Verlag
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-006-6137-8
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process (PDMP). An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen[2], the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Mar 13, 2008