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On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Author

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  • Christian Kasumo
  • Juma Kasozi
  • Dmitry Kuznetsov

Abstract

We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model. To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance. Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind. We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters. Numerical examples with both light- and heavy-tailed distributions are given. The results show that proportional reinsurance increases the survival of the company in both light- and heavy-tailed distributions for the Cramér-Lundberg and diffusion-perturbed models.

Suggested Citation

  • Christian Kasumo & Juma Kasozi & Dmitry Kuznetsov, 2018. "On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-11, February.
    • Handle: RePEc:hin:jnljam:9180780
    DOI: 10.1155/2018/9180780
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    Cited by:

    1. Ragnar Levy Gudmundarson & Manuel Guerra & Alexandra Bugalho de Moura, 2021. "Minimizing ruin probability under dependencies for insurance pricing," Papers 2108.10075, arXiv.org.
    2. R.L. Gudmundarson & M. Guerra & A. B. de Moura, 2021. "Minimizing Ruin Probability Under Dependencies for Insurance Pricing," Working Papers REM 2021/0193, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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