On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance
Loading...
Date
2018-02-22
Authors
Kasumo, Christian
Kasozi, Juma
Kuznetsov, Dmitry
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi
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.
Sustainable Development Goals
This research article published by Hindawi, 2018
Keywords
Research Subject Categories::MATHEMATICS