Article
Version 1
Preserved in Portico This version is not peer-reviewed
Minimizing an Insurer's Ultimate Ruin Probability by Noncheap Proportional Reinsurance Arrangements and Investments
Version 1
: Received: 10 January 2019 / Approved: 14 January 2019 / Online: 14 January 2019 (07:03:01 CET)
Version 2 : Received: 22 January 2019 / Approved: 24 January 2019 / Online: 24 January 2019 (08:52:20 CET)
Version 2 : Received: 22 January 2019 / Approved: 24 January 2019 / Online: 24 January 2019 (08:52:20 CET)
A peer-reviewed article of this Preprint also exists.
Kasumo, C. Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments. Math. Comput. Appl. 2019, 24, 21. Kasumo, C. Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments. Math. Comput. Appl. 2019, 24, 21.
Abstract
In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.
Keywords
ruin probability; jump-diffusion; HJB equation; Volterra equation; block-by-block method; proportional reinsurance; investments
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
