Optimal dividend and risk control strategies for an insurer with two groups of reinsurers

This paper assumes that an insurer can control the dividend, reinsurance and refinancing strategies dynamically, and needs to bear proportional and fixed transaction costs. Different from previous literature, we assume that the insurer can buy reinsurance from two groups of reinsurers, i.e. the first group consists of m reinsurers and the second group consists of n reinsurers. The two groups of reinsurers have different risk attitudes and use the variance premium principle and the exponential premium principle in pricing, respectively. By using the optimal control methods, we obtain the optimal joint strategies for maximizing the insurance company's value. The results prove that dividends should be paid according to the impulse strategy; refinancing should be considered if and only if the transaction costs are not too high and the surplus is null; the insurer should diversify risks to all reinsurers in the market simultaneously when the surplus is not too large. The proportion of risk ceded to each reinsurer depends on its quoted price. Finally, numerical examples and economic interpretations are provided to make illustrations.