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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Numerical Ultimate Ruin Probabilities under Interest Force

Juma Kasozi and Jostein Paulsen

Abstract

This work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method in conjuction with the Simpson rule to solve the Volterra equation for ultimate ruin. This probability is arrived at by taking a linear combination of some two solutions to the Volterra integral equation. The several numerical examples given show that our results are excellent and reliable.

Journal of Mathematics and Statistics
Volume 1 No. 3, 2005, 246-251

DOI: https://doi.org/10.3844/jmssp.2005.246.251

Published On: 30 September 2005

How to Cite: Kasozi, J. & Paulsen, J. (2005). Numerical Ultimate Ruin Probabilities under Interest Force. Journal of Mathematics and Statistics, 1(3), 246-251. https://doi.org/10.3844/jmssp.2005.246.251

Open AccessCopyright: © 2005 Juma Kasozi and Jostein Paulsen. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Risk theory
  • ruin probability
  • volterra integral equation
  • block-by-block method