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On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

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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, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:9180780
    DOI: 10.1155/2018/9180780
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    References listed on IDEAS

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    1. Paulsen, Jostein & Kasozi, Juma & Steigen, Andreas, 2005. "A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 399-420, June.
    2. Jang, Bong-Gyu & Kim, Kyeong Tae, 2015. "Optimal reinsurance and asset allocation under regime switching," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 37-47.
    3. Centeno, Lourdes, 1985. "On Combining Quota-Share and Excess of Loss," ASTIN Bulletin, Cambridge University Press, vol. 15(1), pages 49-63, April.
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    Cited by:

    1. Masoud Komunte & Christian Kasumo & Verdiana Grace Masanja, 2022. "Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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