Singular optimal control models of proportional reinsurance problem
比例再保险问题的奇异型最优控制模型

Two factors, a constant payment of corporate debts and compensatory payment on the insurance companys bankruptcy, are introduced into a proportional reinsurance model with dividend payment, which generates a new class of singular optimal stochastic control models on proportional reinsurance. Effects of the three factors on the companys reserve fund are analyzed by virtue of the methods of stochastic analysis. Moreover, optimal control policies and the corresponding maximal yields in different cases are obtained in explicit forms according to the different relations between the income rate and the debts paid per year.