具有相依理赔量的离散时间风险模型的破产问题
RUIN PROBLEMS FOR THE DISCRETE TIME INSURANCE RISK MODEL WITH THE DEPENDENT CLAIM AMOUNT

本文研究了理赔量具有一阶自回归结构以及在此条件下引入折现率和双险种两种广义离散时间金融风险模型的破产问题.利用数学递推的方法，获得了破产持续时间分布和盈余首次穿过给定水平x的时刻分布所满足的积分方程，并给出当理赔量服从指数分布时相关破产分布的数值分析结果，推广了经典离散时间金融风险模型的结构和破产问题.
In this paper, we consider two sorts of the general discrete-time insurance risk model when the claim amount has the first-order autoregressive structure, then we also consider discount rate and double type risk on the condition of it. Using recursive method and mathematical induction, we can obtain the recursive expressions of the distribution of duration of ruin and the distribution of the moment when the surplus for the first time through an assigned level x. The structure of the classical discrete time financial risk model and ruin problems are generalized