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    On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

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    Date
    2018-02-22
    Author
    Kasumo, Christian
    Kasozi, Juma
    Kuznetsov, Dmitry
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    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 transforminto 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 Cram´er-Lundberg and diffusion-perturbed models.
    URI
    https://doi.org/10.1155/2018/9180780
    http://dspace.nm-aist.ac.tz/handle/123456789/641
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