Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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)

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