on minimizing the ultimate ruin probability of an insurer by reinsurance

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ID: 199915
2018
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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 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.
Reference Key
kasumo2018journalon Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Christian Kasumo;Juma Kasozi;Dmitry Kuznetsov
Journal Chemico-biological interactions
Year 2018
DOI
10.1155/2018/9180780
URL
http://dx.doi.org/10.1155/2018/9180780
Keywords
mathematics

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