Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments
AbstractIn 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
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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. Mathematical and Computational Applications. 2019; 24(1):21.Chicago/Turabian Style
Kasumo, Christian. 2019. "Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments." Math. Comput. Appl. 24, no. 1: 21.
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