相依风险下的信度模型
发布时间：2018-07-27 14:30
【摘要】：在保险公司中，保费定价（预测）是精算师的一个重要的任务。在制定保费的过程中，精算师必须对多保单的风险进行科学的分析和建模，从而制定合适的保费。信度理论是保费定价模型的一种主要的方法。在大部分的保费定价模型中，常常假设风险之间相互独立。这主要是基于简化数学模型的考虑。事实上，由于风险的复杂性，，风险之间常常呈现相依的情形。例如，研究表明，夫妻之间的寿命具有相依性，相邻房屋之间可能面临共同的火灾风险，同一个城市的居民面临相同的地震风险等。 本文主要建立时间变化效应相依和风险之间呈现某种相依情形下的信度模型。在某种相依结构下，得到未来各年的保费预测。并将该模型的方法运用于GDP预测，得到较好的结论。 第二章利用信度理论方法研究了单合同和多合同下具有时间变化效应的风险保费的估计问题。结论表明，具有时间变化效应的信度模型,其信度估计仍然是个体索赔数据与聚合保费的加权平均，且信度因子依赖时间变化效应，从而推广了经典的信度原理。最后，将信度预测的方法运用于中国GDP的预测问题。若将不同的省份看成多个合同，不同年份的GDP数据看成各个合同在各年的索赔额（率），则我国各省的GDP数据恰吻合信度模型的数据结构，我们在时间变化效应相依的信度模型中对2013及以后若干年的数据进行信度预测，结果证明该预测方法有较高的精确度。 在第三章中讨论了风险间相依下的信度模型。注意在经典的Bu¨hlmann信度模型中，各个合同风险被假定为相互独立的。本章假设保险合同的风险之间存在相依性，我们建立了某种特殊相依结构下的Bu¨hlmann信度模型和Bu¨hlmann-Straub信度模型，通过正交投影的方法分别得到对应模型下的未来索赔的信度预测。结论表明，在保险合同之间呈现这种相依结构信度模型，其信度预测仍然是个体索赔数据与聚合保费的加权和。
[Abstract]:In insurance companies, premium pricing (forecasting) is an important task for actuaries. In the process of making premium, the actuary must analyze and model the risk of multiple insurance policies scientifically, so as to make the appropriate premium. Reliability theory is a main method of premium pricing model. In most premium pricing models, risks are often assumed to be independent of each other. This is mainly based on the consideration of simplified mathematical models. In fact, because of the complexity of risk, risk often appears to be dependent on each other. For example, studies have shown that couples' lives depend on each other, that adjacent houses may face the same fire risk, and that residents of the same city may face the same earthquake risk. In this paper, we establish a reliability model in which there is a certain dependence between the time dependent and the risk. Under some dependent structure, the premium forecast for the next year is obtained. The model is applied to GDP prediction, and a good conclusion is obtained. In chapter 2, we use reliability theory to study the estimation of risk premium with time-varying effect under single contract and multi-contract. The results show that the reliability estimation of the reliability model with time-varying effect is still the weighted average of individual claim data and aggregate premium, and the reliability factor depends on the time-varying effect, thus generalizing the classical reliability principle. Finally, the reliability prediction method is applied to the prediction of GDP in China. If different provinces are regarded as multiple contracts, and the GDP data of different years are regarded as the claim amount (rate) of each contract in each year, the GDP data of each province in China coincide with the data structure of the reliability model. In the time-dependent reliability model, we predict the reliability of the data of 2013 and later years. The results show that the method has a high accuracy. In chapter 3, the reliability model of risk dependence is discussed. Note that in the classical Bu-hlmann reliability model, each contract risk is assumed to be independent of each other. In this chapter, assuming that the risks of insurance contracts depend on each other, we establish the Bu-hlmann reliability model and the Bu-hlmann-Straub reliability model under a special dependent structure. The reliability prediction of the future claims under the corresponding model is obtained by orthogonal projection The conclusion shows that the reliability prediction is still the weighted sum of individual claim data and aggregate premium.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67
[Abstract]:In insurance companies, premium pricing (forecasting) is an important task for actuaries. In the process of making premium, the actuary must analyze and model the risk of multiple insurance policies scientifically, so as to make the appropriate premium. Reliability theory is a main method of premium pricing model. In most premium pricing models, risks are often assumed to be independent of each other. This is mainly based on the consideration of simplified mathematical models. In fact, because of the complexity of risk, risk often appears to be dependent on each other. For example, studies have shown that couples' lives depend on each other, that adjacent houses may face the same fire risk, and that residents of the same city may face the same earthquake risk. In this paper, we establish a reliability model in which there is a certain dependence between the time dependent and the risk. Under some dependent structure, the premium forecast for the next year is obtained. The model is applied to GDP prediction, and a good conclusion is obtained. In chapter 2, we use reliability theory to study the estimation of risk premium with time-varying effect under single contract and multi-contract. The results show that the reliability estimation of the reliability model with time-varying effect is still the weighted average of individual claim data and aggregate premium, and the reliability factor depends on the time-varying effect, thus generalizing the classical reliability principle. Finally, the reliability prediction method is applied to the prediction of GDP in China. If different provinces are regarded as multiple contracts, and the GDP data of different years are regarded as the claim amount (rate) of each contract in each year, the GDP data of each province in China coincide with the data structure of the reliability model. In the time-dependent reliability model, we predict the reliability of the data of 2013 and later years. The results show that the method has a high accuracy. In chapter 3, the reliability model of risk dependence is discussed. Note that in the classical Bu-hlmann reliability model, each contract risk is assumed to be independent of each other. In this chapter, assuming that the risks of insurance contracts depend on each other, we establish the Bu-hlmann reliability model and the Bu-hlmann-Straub reliability model under a special dependent structure. The reliability prediction of the future claims under the corresponding model is obtained by orthogonal projection The conclusion shows that the reliability prediction is still the weighted sum of individual claim data and aggregate premium.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;F224;O211.67
【参考文献】
相关期刊论文 前1条
1 温利民;龚海林;王静龙;;具有风险相依结构的B
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