本文選題：溢額再保險 + 復(fù)合Poisson過程�。� 參考：《吉林大學(xué)》2016年碩士論文

【摘要】：保險市場對再保險的需求不斷提高,越來越多的人開始關(guān)注再保險的研究.而風(fēng)險的增大,使得破產(chǎn)概率同樣成為人們研究的重點(diǎn).這時,人們開始關(guān)注再保險的破產(chǎn)概率問題.本文主要研究溢額再保險的破產(chǎn)概率.首先根據(jù)溢額再保險的定義,并用純保費(fèi)原理來計(jì)算保費(fèi),建立如下的模型做為溢額再保險的盈余過程模型：其中c=Aμ.總索賠次數(shù)N(t)分為N1(t)及N2(t)兩部分,沒有發(fā)生再保險的次數(shù)用N1(t)來表示,而發(fā)生溢額再保險的部分則用N2(t)來表示,N1(t)服從參數(shù)為λp的Poisson過程,而N2(t)則服從參數(shù)為λq的Poisson過程,其中p=P(S≤m),且p+q=1.定理1對于盈余過程U(t)來說,最終破產(chǎn)概率為其中R為盈余過程U(t)的調(diào)節(jié)系數(shù),是方程的唯一正根,其中Yi=m/SiXj,Zi=Sj-m.由于模型過于繁瑣,而且不能求得破產(chǎn)概率的清晰表達(dá)式,所以將原保險人在第i次賠付中支付的賠款額表示為而保費(fèi)的計(jì)算則采用期望值原理計(jì)算.那么此時的原保險人的單位保費(fèi)率則變?yōu)槠渲性ｋU人的安全附加保費(fèi)率為θ=c/λμ-1,再保險人的安全附加保費(fèi)率則為η.那么,盈余過程就就可以轉(zhuǎn)變成經(jīng)典風(fēng)險模型的形式,如下則最終破產(chǎn)概率可以表示為其中R為盈余過程U(t)的調(diào)節(jié)系數(shù),是方程的唯一正根.但是此時仍不能獲得破產(chǎn)概率的清晰表達(dá)式,所以用帶漂移的布朗運(yùn)動S1(t)=λμ(m)l-(?)σ(m)Wt,看作S1(t)的擴(kuò)散逼近,其中{Wt,t≥0}是標(biāo)準(zhǔn)布朗運(yùn)動.用S1(t)代替S1(t)帶入模型,我們可以得到新的盈余過程定理2盈余過程Ulm的最終破產(chǎn)概率為其中調(diào)節(jié)系數(shù)為方程g(0)=0的唯一正根.命題3使最小的自留額為
[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，

本文編號：1835226