Next Article in Journal
Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach
Previous Article in Journal
Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle

Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

Department of Science and Mathematics, School of Science, Engineering and Technology, Mulungushi University, P.O. Box 80415 Kabwe, Zambia
Math. Comput. Appl. 2019, 24(1), 21; https://doi.org/10.3390/mca24010021
Received: 9 January 2019 / Revised: 25 January 2019 / Accepted: 28 January 2019 / Published: 2 February 2019
(This article belongs to the Section Social Sciences)
  |  
PDF [553 KB, uploaded 2 February 2019]
  |  

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 a 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 (HJB) 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 individual claim amount 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. View Full-Text
Keywords: ruin probability; jump-diffusion; HJB equation; Volterra equation; block-by-block method; proportional reinsurance; investments ruin probability; jump-diffusion; HJB equation; Volterra equation; block-by-block method; proportional reinsurance; investments
Figures

Figure 1

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 (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Kasumo, C. Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments. Math. Comput. Appl. 2019, 24, 21.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top