基于交替与延迟交替更新过程的随机模糊破产模型研究
发布时间：2018-12-09 13:11
【摘要】：随着世界金融体系的一体化和我国金融体系的进一步开放,我国的金融业特别是作为中国朝阳产业的保险业正面临着前所未有的冲击。破产风险是保险公司压力测试的一个指标,提高破产风险的测量精度对于保险公司的风险控制、保费率厘定和准备金核算等精算问题的研究有非常重要的价值。 本文引入随机模糊变量、交替更新过程和延迟交替更新过程,构建了基于交替与延迟交替更新过程的随机模糊破产模型。论文的主要工作内容及取得的成果包括： 一、定义了随机模糊环境下交替更新过程和延迟交替更新过程,并通过论证得到了几个关于随机模糊环境下的交替更新过程和延迟交替更新过程的重要定理,当交替更新变量和延迟交替更新变量服从随机模糊指数分布时,研究了随机模糊交替更新过程和随机模糊延迟交替更新过程的分布函数、数学期望。 二、构建基于交替更新过程的随机模糊破产模型时引入了随机模糊变量、交替更新过程,当交替更新变量和索赔额变量是服从随机模糊指数分布时,研究了索赔过程的期望、破产时刻的最终破产概率函数和最终破产机会均值。 三、构建基于延迟交替更新过程的随机模糊破产模型时引入了随机模糊变量、延迟交替更新过程,给出了延迟交替更新过程下的最终破产概率概率的一般结论,并且当延迟变量、交替更新变量和索赔额变量是服从随机模糊指数分布时,研究了索赔过程的期望、破产时刻的最终破产概率函数和最终破产机会均值。 四、通过模型仿真和结果分析,揭示了模型的内涵意义和运算机制,将模型仿真结果与保险公司的现实情况进行了对比,进而验证了所构建模型的科学性和实用性,并提出具有建设性的政策建议。 从模型的结构和仿真结果看出交替更新过程与延迟交替更新过程无论从现实意义还是从理论论证角度分析都符合保险公司的赔付过程,将二者定义在随机模糊环境下去研究破产模型,使得模型更具有创新性和前瞻性。
[Abstract]:With the integration of the world financial system and the further opening of China's financial system, China's financial industry, especially the insurance industry as a sunrise industry, is facing an unprecedented impact. Bankruptcy risk is an index of stress testing for insurance companies. Improving the accuracy of bankruptcy risk measurement is of great value to the study of actuarial problems such as risk control, premium rate determination and reserve accounting of insurance companies. In this paper, a stochastic fuzzy ruin model based on alternating and delayed alternating renewal processes is constructed by introducing random fuzzy variables, alternating renewal processes and delayed alternating renewal processes. The main work and achievements are as follows: first, the alternating update process and the delayed alternating update process in random fuzzy environment are defined. Several important theorems about alternating renewal process and delayed alternating renewal process in random fuzzy environment are obtained. When alternating renewal variable and delayed alternating renewal variable are distributed by random fuzzy exponent, The distribution function and mathematical expectation of random fuzzy alternating renewal process and random fuzzy delay alternating renewal process are studied. Secondly, when constructing a stochastic fuzzy ruin model based on alternating renewal process, a stochastic fuzzy variable is introduced. The expectation of the claim process is studied when the alternating renewal variable and the claim amount variable are distributed according to the stochastic fuzzy exponential distribution. The final ruin probability function and the mean of the ultimate ruin opportunity at the ruin time. Thirdly, when constructing the stochastic fuzzy ruin model based on the delayed alternating renewal process, the random fuzzy variables and the delayed alternating renewal process are introduced, and the general conclusion of the final ruin probability under the delayed alternating renewal process is given. When the delay variable, alternate update variable and claim amount variable are distributed from random fuzzy exponent, the expectation of the claim process, the final ruin probability function at the ruin time and the mean value of the ultimate ruin opportunity are studied. Fourthly, through model simulation and result analysis, the connotation significance and operation mechanism of the model are revealed, and the results of model simulation are compared with the actual situation of insurance company, and the scientific and practical nature of the model is verified. And put forward constructive policy suggestions. From the structure of the model and the simulation results, it can be seen that the alternating renewal process and the delayed alternating renewal process are consistent with the insurance company's indemnity process both from the practical significance and from the theoretical point of view. The ruin model is studied by defining them in random fuzzy environment, which makes the model more innovative and forward-looking.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.3
本文编号：2369412
[Abstract]:With the integration of the world financial system and the further opening of China's financial system, China's financial industry, especially the insurance industry as a sunrise industry, is facing an unprecedented impact. Bankruptcy risk is an index of stress testing for insurance companies. Improving the accuracy of bankruptcy risk measurement is of great value to the study of actuarial problems such as risk control, premium rate determination and reserve accounting of insurance companies. In this paper, a stochastic fuzzy ruin model based on alternating and delayed alternating renewal processes is constructed by introducing random fuzzy variables, alternating renewal processes and delayed alternating renewal processes. The main work and achievements are as follows: first, the alternating update process and the delayed alternating update process in random fuzzy environment are defined. Several important theorems about alternating renewal process and delayed alternating renewal process in random fuzzy environment are obtained. When alternating renewal variable and delayed alternating renewal variable are distributed by random fuzzy exponent, The distribution function and mathematical expectation of random fuzzy alternating renewal process and random fuzzy delay alternating renewal process are studied. Secondly, when constructing a stochastic fuzzy ruin model based on alternating renewal process, a stochastic fuzzy variable is introduced. The expectation of the claim process is studied when the alternating renewal variable and the claim amount variable are distributed according to the stochastic fuzzy exponential distribution. The final ruin probability function and the mean of the ultimate ruin opportunity at the ruin time. Thirdly, when constructing the stochastic fuzzy ruin model based on the delayed alternating renewal process, the random fuzzy variables and the delayed alternating renewal process are introduced, and the general conclusion of the final ruin probability under the delayed alternating renewal process is given. When the delay variable, alternate update variable and claim amount variable are distributed from random fuzzy exponent, the expectation of the claim process, the final ruin probability function at the ruin time and the mean value of the ultimate ruin opportunity are studied. Fourthly, through model simulation and result analysis, the connotation significance and operation mechanism of the model are revealed, and the results of model simulation are compared with the actual situation of insurance company, and the scientific and practical nature of the model is verified. And put forward constructive policy suggestions. From the structure of the model and the simulation results, it can be seen that the alternating renewal process and the delayed alternating renewal process are consistent with the insurance company's indemnity process both from the practical significance and from the theoretical point of view. The ruin model is studied by defining them in random fuzzy environment, which makes the model more innovative and forward-looking.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.3
【参考文献】
相关期刊论文 前10条
1 郑敏衡;邓迎春;周杰明;;负二项过程下负风险模型的破产概率[J];湖南文理学院学报(自然科学版);2011年02期
2 葛明星;;一类厚尾延迟更新风险模型的破产概率[J];高师理科学刊;2011年04期
3 王广华;吕玉华;;保费收入随机化的风险模型[J];经济数学;2006年03期
4 张冕;;一类相依的双险种风险模型的破产问题[J];经济数学;2007年04期
5 殷利平;王乃和;吕玉华;;一类索赔时间间隔服从混合指数分布的更新风险过程[J];经济数学;2008年02期
6 郭东林;刘永利;;延迟更新风险模型有限时间的破产概率[J];江西科学;2010年05期
7 吕靖;李俊平;刘志峰;覃东君;;复合二项-负二项风险模型的研究[J];数学理论与应用;2011年02期
8 徐光辉,何启明;交替更新过程的剩余寿命[J];科学通报;1990年11期
9 兰德新;温倩;;一类交错风险过程的破产概率的递推计算[J];南平师专学报;2006年04期
10 温玉珍;张颖;;一类延迟更新风险模型中的罚金函数[J];曲阜师范大学学报(自然科学版);2010年02期
相关博士学位论文 前1条
1 黄涛;随机模糊环境下的破产风险模型[D];天津大学;2009年
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