Optimal risk and dividend strategies with transaction costs and terminal value

- This paper investigates an optimal dividend, refinancing and reinsurance problem with an arbitrary terminal value
- The optimal dividend distribution policy is of barrier type when the dividend rate is unrestricted
- The optimal dividend distribution policy is of threshold type when the dividend rate is bounded
- Refinancing should be considered if and only if the terminal value and the transaction costs are not too high
- The optimal ceded proportion of risk decreases with the current surplus

This paper assumes that an insurance company can control the surplus by paying dividends, raising money and buying proportional reinsurance dynamically. The reinsurance premium is assumed to be calculated via the variance premium principle. Under the objective of maximizing the insurance company's value, we identify the optimal joint strategies and consider the effects of transaction costs and arbitrary terminal value at bankruptcy. From the results, we see that refinancing should be considered if and only if the terminal value and the transaction costs are not too high and the company is on the brink of bankruptcy, and the amount of each capital injection remains constant; the optimal ceded proportion of risk decreases with the current surplus and remains constant when the surplus exceeds some constant level; the optimal dividend distribution policy is of barrier type when the dividend rate is unrestricted or is of threshold type when the dividend rate is bounded, respectively. In particular, the insurance company should declare bankruptcy as soon as possible if the terminal value is high enough.