# Ruin probabilities of a surplus process described by PDMPs

Ruin probabilities of a surplus process described by PDMPs 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, 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Ruin probabilities of a surplus process described by PDMPs

, Volume 24 (1) – Mar 13, 2008
12 pages      /lp/springer-journals/ruin-probabilities-of-a-surplus-process-described-by-pdmps-d0Ds5v0TXN
Publisher
Springer Journals
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, 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 SinicaSpringer Journals

Published: Mar 13, 2008

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