Translator Disclaimer
2018 On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance
Christian Kasumo, Juma Kasozi, Dmitry Kuznetsov
J. Appl. Math. 2018: 1-11 (2018). DOI: 10.1155/2018/9180780

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.

Citation

Download Citation

Christian Kasumo. Juma Kasozi. Dmitry Kuznetsov. "On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance." J. Appl. Math. 2018 1 - 11, 2018. https://doi.org/10.1155/2018/9180780

Information

Received: 28 November 2017; Revised: 19 January 2018; Accepted: 30 January 2018; Published: 2018
First available in Project Euclid: 17 March 2018

zbMATH: 07132110
MathSciNet: MR3770640
Digital Object Identifier: 10.1155/2018/9180780

Rights: Copyright © 2018 Hindawi

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.2018 • 2018
Back to Top