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On Ultimate Ruin in a Delayed-Claims Risk Model

  • Kam C. Yuen (a1), Junyi Guo (a2) and Kai W. Ng (a1)

Abstract

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.

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Copyright

Corresponding author

Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
∗∗ Email address: kcyuen@hku.hk
∗∗∗ Postal address: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China.

References

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Grandell, J. (1977). A class of approximations of ruin probabilities. Scand. Actuarial J., 3752.
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Waters, H. R. and Papatriandafylou, A. (1985). Ruin probabilities allowing for delay in claims settlement. Insurance Math. Econom. 4, 113122.
Yuen, K. C. and Guo, J. Y. (2001). Ruin probabilities in the binomial model with time-correlated aggregate claims. Insurance Math. Econom. 29, 4757.

Keywords

MSC classification

On Ultimate Ruin in a Delayed-Claims Risk Model

  • Kam C. Yuen (a1), Junyi Guo (a2) and Kai W. Ng (a1)

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