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Total duration of negative surplus for the compound Poisson process that is perturbed by diffusion

Part of: Markov processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Chunsheng Zhang  and
Rong Wu
Chunsheng Zhang*
Affiliation:
Nankai Universit
Rong Wu*
Affiliation:
Nankai Universit
*
∗ Postal address: Institute of Mathematics Science, Nankai University, Tianjin 300071, China.
∗ Postal address: Institute of Mathematics Science, Nankai University, Tianjin 300071, China.
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Abstract

In this paper, we consider the compound Poisson process that is perturbed by diffusion (CPD). We derive formulae for the Laplace transform, expectation and variance of total duration of negative surplus for the CPD and also present some examples of the CPD with an exponential individual claim amount distribution and a mixture exponential individual claim amount distribution.

Keywords

Laplace transformsprobability and severity of ruinnegative surplus excursiontotal duration of negative surplusWiener process

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60J60: Diffusion processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 517 - 532
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Supported by NNSF grant number 19971047.

References

Dufresne, F., and Gerber, H. U. (1991). Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance Math. Econom. 10, 51–59.CrossRefGoogle Scholar
Egídio dos Reis, A. D. (1993). How long is the surplus below zero? Insurance Math. Econom. 12, 23–38.CrossRefGoogle Scholar
Gerber, H. U. (1990). When does the surplus reach a given target? Insurance Math. Econom. 9, 115–119.CrossRefGoogle Scholar
Ikeda, N., and Watanabe, E. S. (1981). Stochastic Differential Equations and Diffusion Process. North-Holland, Amsterdam.Google Scholar
Schäl, M. (1993). On the hitting times for jump-diffusion processes with past dependent local characteristics. Stoch. Process. Appl. 47, 131–142.CrossRefGoogle Scholar