溢额再保险破产概率的近似计算

发布时间：2018-05-02 19:42

  本文选题：溢额再保险 + 复合Poisson过程　； 参考：《吉林大学》2016年硕士论文

【摘要】：保险市场对再保险的需求不断提高,越来越多的人开始关注再保险的研究.而风险的增大,使得破产概率同样成为人们研究的重点.这时,人们开始关注再保险的破产概率问题.本文主要研究溢额再保险的破产概率.首先根据溢额再保险的定义,并用纯保费原理来计算保费,建立如下的模型做为溢额再保险的盈余过程模型：其中c=Aμ.总索赔次数N(t)分为N1(t)及N2(t)两部分,没有发生再保险的次数用N1(t)来表示,而发生溢额再保险的部分则用N2(t)来表示,N1(t)服从参数为λp的Poisson过程,而N2(t)则服从参数为λq的Poisson过程,其中p=P(S≤m),且p+q=1.定理1对于盈余过程U(t)来说,最终破产概率为其中R为盈余过程U(t)的调节系数,是方程的唯一正根,其中Yi=m/SiXj,Zi=Sj-m.由于模型过于繁琐,而且不能求得破产概率的清晰表达式,所以将原保险人在第i次赔付中支付的赔款额表示为而保费的计算则采用期望值原理计算.那么此时的原保险人的单位保费率则变为其中原保险人的安全附加保费率为θ=c/λμ-1,再保险人的安全附加保费率则为η.那么,盈余过程就就可以转变成经典风险模型的形式,如下则最终破产概率可以表示为其中R为盈余过程U(t)的调节系数,是方程的唯一正根.但是此时仍不能获得破产概率的清晰表达式,所以用带漂移的布朗运动S1(t)=λμ(m)l-(?)σ(m)Wt,看作S1(t)的扩散逼近,其中{Wt,t≥0}是标准布朗运动.用S1(t)代替S1(t)带入模型,我们可以得到新的盈余过程定理2盈余过程Ulm的最终破产概率为其中调节系数为方程g(0)=0的唯一正根.命题3使最小的自留额为
[Abstract]:With the increasing demand for reinsurance in the insurance market, more and more people begin to pay attention to the research of reinsurance. And the increase of risk makes the probability of bankruptcy also become the focus of research. At this time, people began to pay attention to the probability of reinsurance bankruptcy. This paper mainly studies the ruin probability of excess reinsurance. Firstly, according to the definition of excess reinsurance, and using the pure premium principle to calculate the premium, the following model is established as the surplus process model of excess reinsurance: where cu 渭. The total number of claims is divided into two parts, N _ 1t) and N _ 2T). The number of times of no reinsurance is expressed by the number of times of reinsurance, while the part of the reinsurance of excess amount is represented by the Poisson process with 位 _ p parameter, while the Poisson process with 位 _ Q parameter is taken by N _ 2t). Where the p=P(S is 鈮，

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