带有多索赔情形风险模型的破产概率

发布时间：2018-05-11 04:19

本文选题：破产概率 + 生存概率　；参考：《河南师范大学》2017年硕士论文

【摘要】：在实际的保险业务中,保险公司不仅会开展多险种业务,而且许多险种的索赔也不是只有一种,存在单一险种的多索赔的情形.本文以此为出发点考虑了带有多索赔情形的风险模型,主要研究内容如下:(1)考虑了一类带干扰的单险种多索赔情形的风险模型.假设保单到达过程为Poisson过程,各情形索赔到达过程为保单到达过程的随机p^稀疏过程,首先证明了调节系数的存在唯一性,然后利用鞅的不等式及性质,得到了该模型下破产概率的Lundberg不等式及一般表达式.(2)考虑了一类多险种多索赔情形的风险模型.首先,得到了破产概率的Lund-berg不等式及一般表达式.然后,通过模型转换,考虑充分小时段内的索赔情况,利用全概率公式得到了生存概率所满足的积分-微分方程.最后.考虑两险种且索赔额服从指数分布这一特定情况,结合前面得到的积分-微分方程和经典风险理论的结果,给出了该特定情况下破产概率的显式表达式.(3)考虑了一类两险种多索赔情形的相依风险模型.前面几节,研究了索赔过程都为Poisson过程的情形,得到了破产概率的Lundberg不等式及一般表达式,生存概率的积分-微分方程和索赔额服从指数分布情形下的破产概率显示表达式.最后,对原风险模型的相依部分进行了一些转变,得到了破产概率的一些结果.
[Abstract]:In the actual insurance business, the insurance company will not only carry out multi-insurance business, but also many kinds of insurance claims are not only one, there is a single type of multi-claim situation. In this paper, a risk model with multiple claims is considered. The main contents of this study are as follows: (1) the risk model of a class of single-type multiple claims with interference is considered. Assuming that the policy arrival process is a Poisson process and the claim arrival process is a stochastic p ^ sparse process of the policy arrival process, the existence and uniqueness of the adjustment coefficient are first proved, and then the martingale inequality and properties are used. The Lundberg inequality and general expression of ruin probability under this model are obtained. Firstly, the Lund-berg inequality and general expression of ruin probability are obtained. Then, through the model transformation, considering the claim in sufficient small period, the integro-differential equation of survival probability is obtained by using the full probability formula. Finally. Considering the special case of two kinds of insurance and the exponential distribution of the claimed amount, combining the results of the previous integro-differential equation and classical risk theory, In this paper, the explicit expression of ruin probability in this particular case is given. The dependent risk model for a class of multi-claim cases with two types of insurance is considered. In the previous sections, we studied the case that the claim process is a Poisson process, obtained the Lundberg inequality and the general expression of the ruin probability, the integro-differential equation of the survival probability and the expression of the ruin probability under the condition of exponential distribution of the claim amount. Finally, some changes are made to the dependent parts of the original risk model, and some results of the ruin probability are obtained.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840.4

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