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Survival probability for a two-dimensional risk model

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  • Dang, Lanfen
  • Zhu, Ning
  • Zhang, Haiming

Abstract

In this paper, we consider the survival probability for a two-dimensional risk model. We derive a partial integro-differential equation satisfied by the survival probability and prove its differentiability. We obtain explicit expressions for recursively calculating the survival probability by applying the partial integro-differential equation when claims are exponentially distributed.

Suggested Citation

  • Dang, Lanfen & Zhu, Ning & Zhang, Haiming, 2009. "Survival probability for a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 491-496, June.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:3:p:491-496
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    References listed on IDEAS

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    1. Ambagaspitiya, Rohana S., 2003. "Aggregate survival probability of a portfolio with dependent subportfolios," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 431-443, July.
    2. Ambagaspitiya, Rohana S., 1999. "On the distributions of two classes of correlated aggregate claims," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 301-308, May.
    3. Wang, Guojing & Wu, Rong, 2001. "Distributions for the risk process with a stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 329-341, October.
    4. Wang, Guojing & Yuen, Kam C., 2005. "On a correlated aggregate claims model with thinning-dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 456-468, June.
    5. Wu, Xueyuan & Yuen, Kam C., 2003. "A discrete-time risk model with interaction between classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 117-133, August.
    6. Chan, Wai-Sum & Yang, Hailiang & Zhang, Lianzeng, 2003. "Some results on ruin probabilities in a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 345-358, July.
    7. Cossette, Helene & Marceau, Etienne, 2000. "The discrete-time risk model with correlated classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 133-149, May.
    8. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2002. "On a correlated aggregate claims model with Poisson and Erlang risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 205-214, October.
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    Cited by:

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    3. Albrecher, Hansjörg & Cheung, Eric C.K. & Liu, Haibo & Woo, Jae-Kyung, 2022. "A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 96-118.
    4. Gong, Lan & Badescu, Andrei L. & Cheung, Eric C.K., 2012. "Recursive methods for a multi-dimensional risk process with common shocks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 109-120.
    5. Florin Avram & Romain Biard & Christophe Dutang & Stéphane Loisel & Landy Rabehasaina, 2014. "A survey of some recent results on Risk Theory," Post-Print hal-01616178, HAL.
    6. Wang, Guanqing & Wang, Guojing & Yang, Hailiang, 2016. "On a multi-dimensional risk model with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 73-83.
    7. Liu, Jingchen & Woo, Jae-Kyung, 2014. "Asymptotic analysis of risk quantities conditional on ruin for multidimensional heavy-tailed random walks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 1-9.
    8. Zhang, Yuanyuan & Wang, Wensheng, 2012. "Ruin probabilities of a bidimensional risk model with investment," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 130-138.

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