基于交替更新过程的随机模糊破产模型

The Random Fuzzy Ruin Model Based on Alternating Renewal Process

构建一个更能刻画保险公司现实运营状况的破产模型,对于保险公司来说具有重要意义。假设索赔额、盈余额和更新过程均是在随机模糊环境下,使得该模型不仅能反映事件的随机性,也能反映决策者的主观性;同时,假设保险公司赔偿时刻滞后与核赔事件发生时刻,建立了交替更新过程。基于以上两点假设,当索赔额和时间间隔均是服从指数分布时,建立了交替更新过程下的随机模糊破产模型,并给出了最终破产概率公式与最终破产机会均值公式。

The establishment of a ruin model is very important to insurance, especially in the aspect of rate setting and reserve accounting. In the paper, claim amount, earnings amount and alternating renewal process were assumed on a random fuzzy basis. Therefore, the randomness of events and the subjectivity of decision makers were consid- ered in the model. At the same time, the paper assumed that the time of compensation by insurance company lagged behind time of the incident, and therefore the alternating renewal process was applied in the model. Based on these two types of assumptions, the paper arrived at an ultimate ruin probability formula and formula of chance mean value of ultimate ruin when claim amount and time interval were consistent with the exponential distribution.