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A perturbed risk model with dependence between premium rates and claim sizes

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  • Zhou, Ming
  • Cai, Jun

Abstract

This paper considers a dependent risk model with diffusion for the surplus of an insurer, in which a current premium rate will be adjusted after a claim occurs and the adjusted rate is determined by the amount of the claim. At the same time, the diffusion is changed correspondingly. Using Rouché's theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model. 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 recursion expression for the survival probability, by which we can exactly solve the survival probability step-by-step. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

Suggested Citation

  • Zhou, Ming & Cai, Jun, 2009. "A perturbed risk model with dependence between premium rates and claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 382-392, December.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:382-392
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    References listed on IDEAS

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    1. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
    2. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
    3. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    4. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    5. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 391-408, June.
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    2. Matija Vidmar, 2016. "Ruin under stochastic dependence between premium and claim arrivals," Papers 1602.04580, arXiv.org, revised Jun 2017.
    3. Franck Adékambi & Essodina Takouda, 2022. "On the Discounted Penalty Function in a Perturbed Erlang Renewal Risk Model With Dependence," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 481-513, June.

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