Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle

•The combined optimal dividend, capital injection and reinsurance problems are investigated.•The reinsurance premium is calculated according to the variance principle.•The proportional and fixed transaction costs and the salvage value are taken into account.•Explicit solutions for the value functions and the optimal strategies are obtained.

In this paper we study the combined optimal dividend, capital injection and reinsurance problems in a dynamic setting. The reinsurance premium is assumed to be calculated via the variance principle instead of the expected value principle. The proportional and fixed transaction costs and the salvage value at bankruptcy are included in the model. In both cases of unrestricted dividend rate and restricted dividend rate, we obtain the closed-form solutions of the value function and the optimal joint strategies, which depend on the transaction costs and the profitability in future.