中文摘要：

将保险公司各期净损失相互独立的假定改进为依随机序正相依.在相依风险下,利用动态规划原理和状态空间约简,刻画了最优分红策略,证明了区域策略最优,同时讨论了值函数的性质,并给出了数值算法.其中,对涉及独立假定的结论,给出了相依条件下的相应结果,对未涉及独立假定的部分结论也做了改进.研究发现,与独立情形不同,在依随机序正相依风险下,保险公司不必以概率1破产.

英文摘要：

The independence assumption of net loss for each period of insurance company is improved to be positively dependent through the stochastic ordering.With dependent risks,applying the dynamic programming principle and state-space reduction,the optimal dividend strategies are characterized,the optimality of band policy is proved.In the meantime,the properties of value function are discussed,and the numerical algorithm is given.Where,for the conclusions involving independence assumption,the corresponding results under the dependence condition are given,and for parts of the conclusions not involving independence assumption,improvements are made.Research also finds that the insurance company need not ruin with probability 1 under the condition of positive dependence through the stochastic ordering,which is different from the situation of independence.