利率服从AR( m )离散 时间风险模型的破产分布

研究当保费收入在时间区间的期初和期末给付时的两种广义的离散时间的风险模型，当保险公司的利率具有 m 阶自回归结构的情况下，将其代入上述模型通过递推和数学归纳法 ，分别得到了描述破产问题的破产前最大盈余分布，破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平 x 的时间分布的满足的微分方程，最后指出可以结合具体的例子会有比较好的实际价值.

Ruin Problems for the Discrete Time Insurance Risk Model With Autoregressive Structure of Morder Dependent Rate

We discussed two sorts of general discrete time insurance risk models when the insurance fee gains at the beginning of the time zone and in the end of the period.In the models, the rates of interest were assumed to have a dependent autoregressive structure of m order.We put it in the two models, and by the recursion and the mathematic method, we derived some recursive expressions of the supremum surplus before ruin and the joint distribution of surplus before ruin and deficit after ruin and supremum surplus before ruin.The time that the surplus process reaches a given level x for the first time was obtained, which describes the bankruptcy problems.Finally, it is pointed that we can get the better practice value if we combine the models with concrete examples.