%0 Journal Article
%T Minimizing an Insurer¡¯s Ultimate Ruin Probability by Reinsurance and Investments
%J Mathematical and Computational Applications | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/mca24010021
%X 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¨CScholes 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¨CJacobi¨CBellman (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-Tex
%U https://www.mdpi.com/2297-8747/24/1/21