On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Christian Kasumo, Juma Kasozi and Dmitry Kuznetsov

Journal of Applied Mathematics, 2018, vol. 2018, issue 1

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.

Date: 2018
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https://doi.org/10.1155/2018/9180780

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2018:y:2018:i:1:n:9180780

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