Optimal risk management strategies in a diffusion risk process: a simultaneous problem

Abouzar Bazyari

Scandinavian Actuarial Journal, 2025, vol. 2025, issue 7, 718-740

Abstract: Different to previous studies, this paper studies the optimal risk management strategies with consideration of reinsurance strategies together with capital injections simultaneously for two insurance companies according to a diffusion approximation risk model whose cash surpluses are modeled with a Brownian motion and reinsurance premium rate. Our focus is on the possibility for two insurance companies to rely on reinsurance premium rate to bring the surplus difference process back to a given level if it has fallen below it and study the optimization problem in the financial market in order to maximize the insurance companies profitability. We formulate the surplus processes based on the capital injections and reinsurance by using the techniques of diffusion approximation. The explicit expressions for optimal reinsurance strategies of two insurance companies are obtained for the controlled operator function of proposal strategies with quadratic form of reinsurance premium rate. The optimal capital injection strategies are computed in the present of reflecting the surplus difference of two insurance risk processes at the upper and lower thresholds. Moreover, using It $ \hat o $ oˆ formula the risk optimization problem is solved in our risk problem. Finally, numerical analyses are conducted to illustrate the effects of model parameters on the optimal risk management strategies.

Date: 2025
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DOI: 10.1080/03461238.2025.2457098

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