鞅在保险精算中的应用

发布时间：2018-06-03 20:02

本文选题：鞅 + 破产概率　；参考：《重庆理工大学》2013年硕士论文

【摘要】：在保险精算中，破产论是保险精算的重要组成部分，破产论研究的核心问题是通过破产概率这一量化的指标来衡量保险公司的运营情况。破产概率是指保险公司盈余资金为负值的概率，破产概率可以作为保险公司风险评估的依据，因此对保险公司和保险监督部门有极为重要的指导作用。近几年来，鞅作为一种有力的研究理论工具逐渐向各个学科领域渗透。借助鞅这个理论工具来研究保险精算中的风险模型，具有很高的实用价值。文章的研究内容主要分为两个部分：第一，一般的破产理论中，处理盈余过程时常常未考虑利率的因素，或者是在常利率的条件下考虑破产概率问题。但事实上，，受外部经济因素的影响，随机利率会更符合实际情况。本文讨论的保险公司破产概率，是指在随机利率的条件下，对离散的风险模型，利用鞅论的方法得到最终破产概率的指数型上界。第二，通过鞅论得到破产概率上界，保险人以破产概率为准则，通过再保险策略使自身风险达到最小值，通过更新过程来描述聚合风险，破产概率的上界由调节系数给定，而这里的调节系数可视为超额损失再保险自留额的函数，通过对该函数的分析，得出针对保险人最优的自留额，使得破产概率上界达到最小。
[Abstract]:In actuarial insurance, bankruptcy theory is an important part of actuarial insurance. The core problem of bankruptcy theory research is to measure the operation of insurance companies through the quantitative index of bankruptcy probability. The probability of bankruptcy is the probability that the surplus capital of insurance company is negative, and the probability of bankruptcy can be used as the basis of risk assessment of insurance company, so it plays an important role in guiding the insurance company and the insurance supervision department. In recent years, martingale, as a powerful theoretical tool, has gradually penetrated into various disciplines. It is of great practical value to study the risk model in actuarial insurance by means of martingale. The research content of this paper is divided into two parts: Firstly, in general bankruptcy theory, the factor of interest rate is often not taken into account when dealing with the surplus process, or the ruin probability is considered under the condition of constant interest rate. But in fact, the impact of external economic factors, random interest rates will be more in line with the actual situation. The ruin probability of insurance companies discussed in this paper is to obtain the exponential upper bound of the final ruin probability for discrete risk models under the condition of random interest rate by means of martingale theory. Secondly, the upper bound of ruin probability is obtained by martingale theory, the insurer takes ruin probability as the criterion, the risk is minimized by reinsurance strategy, and the aggregation risk is described by updating process. The upper bound of ruin probability is given by the adjustment coefficient. The adjustment coefficient can be regarded as a function of the retention amount of excess loss reinsurance. Through the analysis of the function, the optimal retention amount for the insurer is obtained, and the upper bound of the ruin probability is minimized.
【学位授予单位】：重庆理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.4;O211.6

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