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On Ultimate Ruin in a Delayed-Claims Risk Model

Published online by Cambridge University Press:  14 July 2016

Kam C. Yuen*
Affiliation:
The University of Hong Kong
Junyi Guo*
Affiliation:
Nankai University
Kai W. Ng*
Affiliation:
The University of Hong Kong
*
Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
∗∗∗Postal address: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China.
Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

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In this paper, we consider a risk model in which each main claim induces a delayed claim called a by-claim. The time of delay for the occurrence of a by-claim is assumed to be exponentially distributed. From martingale theory, an expression for the ultimate ruin probability can be derived using the Lundberg exponent of the associated nondelayed risk model. It can be shown that the Lundberg exponent of the proposed risk model is the same as that of the nondelayed one. Brownian motion approximations for ruin probabilities are also discussed.

Type
Research Papers
Copyright
© Applied Probability Trust 2005 

References

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