关于非寿险中的免赔额问题研究
发布时间：2018-08-17 14:22
【摘要】：保险公司为了管控风险,通常采取各种策略以便分散风险,降低成本,比如,对某类险种设置免赔额,或者再保险分出等措施,使其增强经营的稳定性。但如何根据风险损失分布和投保人的承担能力确定合理的份额一直是人们研究的热点问题。同时,基于投保人的愿望,在支付保费承受能力的限制下,如何合理确定自担份额也是其热切需求的。 本文首先对国内外非寿险的免赔额研究情况进行了总结,并引入了破产概率和效用函数两种新的风险度量指标来分析和解决非寿险的免赔额问题。同时了解了损失次数分布和损失金额分布情况,为解决非寿险的免赔额问题奠定基础。 其次,研究在有免赔额下的风险盈余过程,并推导出具有免赔额下的破产概率微分积分方程。在损失分布为指数分布下,给出破产概率的显式解,并在此基础上,当免赔额变动时分析其对破产概率的影响。 第三,本文借鉴前一问题的思想,基于投保人的效用函数,研究了投保人的风险分散转移问题,即选择合理自留额和转嫁的投保份额。为此,以投保人的效用函数为目标建立优化模型,在损失分布为Pareto分布下,给出数值解,并根据实例数据作出分析,得出了能够使投保人和保险人共同认可,且达到双赢的效果的一个相对最优的免赔额,证明了本文所采用的计算方法是可行的。
[Abstract]:In order to control risks, insurance companies usually take a variety of strategies to disperse risks and reduce costs, such as deductible for certain types of insurance, or reinsurance to enhance the stability of the operation. However, how to determine the reasonable share according to the risk loss distribution and the ability of the insured has always been a hot issue. At the same time, on the basis of the policy holder's desire, how to reasonably determine the share of one's own is also the eager demand under the limit of the ability to pay the premium. This paper first summarizes the research on deductible amount of non-life insurance at home and abroad, and introduces two new risk metrics, bankruptcy probability and utility function, to analyze and solve the deductible amount of non-life insurance. At the same time, the distribution of loss times and loss amount is understood, which lays the foundation for solving the problem of non-life insurance deductible. Secondly, the risk surplus process with deductible amount is studied, and the ruin probability differential integral equation with deductible amount is derived. When the loss distribution is exponential, the explicit solution of ruin probability is given, and on this basis, the influence of loss distribution on ruin probability is analyzed when the deductible amount changes. Thirdly, based on the utility function of the policy holder, this paper studies the risk dispersion transfer problem of the policy holder, that is, choosing the reasonable retention amount and the transferred insurance share. Therefore, the optimization model is established with the utility function of the insured as the objective. When the loss is distributed as Pareto distribution, the numerical solution is given, and the analysis is made according to the example data, and it is concluded that the policy holder and the insurer can agree with each other. And a relatively optimal deductible is obtained, which proves that the calculation method is feasible.
【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840.3
本文编号：2187910
[Abstract]:In order to control risks, insurance companies usually take a variety of strategies to disperse risks and reduce costs, such as deductible for certain types of insurance, or reinsurance to enhance the stability of the operation. However, how to determine the reasonable share according to the risk loss distribution and the ability of the insured has always been a hot issue. At the same time, on the basis of the policy holder's desire, how to reasonably determine the share of one's own is also the eager demand under the limit of the ability to pay the premium. This paper first summarizes the research on deductible amount of non-life insurance at home and abroad, and introduces two new risk metrics, bankruptcy probability and utility function, to analyze and solve the deductible amount of non-life insurance. At the same time, the distribution of loss times and loss amount is understood, which lays the foundation for solving the problem of non-life insurance deductible. Secondly, the risk surplus process with deductible amount is studied, and the ruin probability differential integral equation with deductible amount is derived. When the loss distribution is exponential, the explicit solution of ruin probability is given, and on this basis, the influence of loss distribution on ruin probability is analyzed when the deductible amount changes. Thirdly, based on the utility function of the policy holder, this paper studies the risk dispersion transfer problem of the policy holder, that is, choosing the reasonable retention amount and the transferred insurance share. Therefore, the optimization model is established with the utility function of the insured as the objective. When the loss is distributed as Pareto distribution, the numerical solution is given, and the analysis is made according to the example data, and it is concluded that the policy holder and the insurer can agree with each other. And a relatively optimal deductible is obtained, which proves that the calculation method is feasible.
【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840.3
【参考文献】
相关期刊论文 前3条
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3 曹玉松;;比例再保险临界比例研究——基于效用函数[J];现代商贸工业;2013年01期
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