Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE PROBABILITY OF RUIN IN A CONTINUOUS RISK MODEL WITH DELAYED CLAIMS

  • Zou, Wei (Department of Science NanChang Institute of Technology) ;
  • Xie, Jie-Hua (Department of Science NanChang Institute of Technology)
  • Received : 2012.01.10
  • Published : 2013.01.01
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Abstract

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

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References

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