Abstract
This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process.
Highlights
The expansion of the economic activities in the sense of time and space triggered the need for managing the exposure to risk for different types of businesses (Aniunas et al [1], Lakstutiene et al [2], and Kurach [3])
This paper investigated the optimal control problem for an insurance company with transaction costs and salvage value where the company controls the risk exposure by the excess-of-loss reinsurance and capital injection based on the symmetry of risk information
The fixed cost incurred by capital injection is incorporated
Summary
The expansion of the economic activities in the sense of time and space triggered the need for managing the exposure to risk for different types of businesses (Aniunas et al [1], Lakstutiene et al [2], and Kurach [3]). Meng et al [8] who studied an optimal dividend problem taking nonlinear insurance risk processes into consideration. Reinsurance is considered an effective method for a company to control its risk exposure This is because an appropriate reinsurance strategy can protect a company against the potentially large loss and, reduce the earning volatility. We add the fixed and proportional transaction cost incurred by capital injection and the salvage value of the company at the ruin time into the surplus process. After identifying the corresponding solutions to these two auxiliary models and the corresponding optimal strategy, we solve the general control problem without any restrictions on capital injection or the surplus process.
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