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On Ultimate Ruin in a Delayed-Claims Risk Model

Part of: Applications Markov processes Stochastic analysis Special processes

Published online by Cambridge University Press:  14 July 2016

Kam C. Yuen ,
Junyi Guo  and
Kai W. Ng
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.

Keywords

Brownian motionby-claimLundberg exponentmain claimmartingaleultimate ruin probabilityweak convergence

MSC classification

Secondary: 60J65: Brownian motion 62P05: Applications to actuarial sciences and financial mathematics 60H05: Stochastic integrals 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 163 - 174
Copyright
© Applied Probability Trust 2005 

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