Optimal proportional reinsurance model with debt liabilities and bankruptcy value

The results of Taksar and Hunderup (2007) are. extended to the case of a constant liability payment delta. The dynamics of an insurance company's surplus is modeled as a diffusion process with constant drift and diffusion coefficient. The objective is to find a policy maximizing the total discounted value of dividends and the bankruptcy value P of the company. By means of stochastic control theory, it is found that if the ratio of the maximal possible expected profit to delta is small, the optimal policy is not to take reinsurance, otherwise the optimal fraction of reinsurance as a function of the current surplus and P monotonically increases to 1 for some constant determined by exogenous parameters and P.