Optimal dividend and scale of business strategies with reinsurance and premium pricing for insurance company

This paper investigates the optimal dividend and business scale strategies aimed at maximizing the value of an insurance company. While prior studies typically assume that insurers can only adjust their business scale through reinsurance, this study extends the framework by allowing the insurer to control the premium rate. Under more realistic market assumptions, we examine the joint optimization problem for two common types of reinsurance—proportional and excess-of-loss—across both arbitrage and non-arbitrage scenarios. We derive the optimal strategies for dividends and premium pricing, along with their corresponding value functions. The results show that the insurer should decrease the premium rate and reduce reinsurance coverage as the surplus increases. The optimal dividend policy follows a barrier strategy. Economic interpretations and numerical examples are provided to illustrate the findings.