【摘要】：隨著保險(xiǎn)業(yè)的快速發(fā)展,保險(xiǎn)公司經(jīng)營(yíng)規(guī)模不斷擴(kuò)大,險(xiǎn)種也趨于多樣化和相依化,只考慮含有一種險(xiǎn)種的風(fēng)險(xiǎn)模型已經(jīng)不能滿(mǎn)足保險(xiǎn)公司的風(fēng)險(xiǎn)管理需求,因此需要將多個(gè)險(xiǎn)種聯(lián)合起來(lái),綜合考慮保險(xiǎn)公司的風(fēng)險(xiǎn)情況,而保險(xiǎn)公司的險(xiǎn)種的索賠次數(shù)之間往往又具有某種相關(guān)性,因此結(jié)合保險(xiǎn)公司實(shí)際運(yùn)營(yíng),對(duì)相依的多險(xiǎn)種模型的破產(chǎn)問(wèn)題進(jìn)行研究,無(wú)論對(duì)保險(xiǎn)公司經(jīng)營(yíng),還是對(duì)監(jiān)督部門(mén)的監(jiān)管,都具有十分重要的意義。 為此,考慮一種稀疏相依的雙險(xiǎn)種風(fēng)險(xiǎn)模型：假定N1(t)=N11(t)+N21(t),N2(t)=N22(t)+N12(t),{N11(t),t0}為參數(shù)為λ11的Poisson過(guò)程,相應(yīng)的{N12(t),t0}是{N11(t),t0}的一個(gè)p1-稀疏過(guò)程,{N22(t),t0}是參數(shù)為λ22的Poisson過(guò)程,相應(yīng)的{N21(t),t0}是{N22(t),t0}的一個(gè)p2-稀疏過(guò)程,Poisson過(guò)程{N22(t),t0}與{N11(t),t0}相互獨(dú)立。首先,將兩個(gè)模型結(jié)合成一個(gè)模型,建立了索賠次數(shù)稀疏相依的風(fēng)險(xiǎn)模型,對(duì)模型破產(chǎn)概論進(jìn)行了研究,同時(shí)討論了稀疏性強(qiáng)弱對(duì)保費(fèi)收取以及破產(chǎn)概論的影響；其次,將模型視為一個(gè)兩維稀疏相依的風(fēng)險(xiǎn)模型,得出了生存概率滿(mǎn)足的偏積分微分方程,并且就指數(shù)分布條件之下,給出了計(jì)算生存概率的一個(gè)迭代算法。
[Abstract]:With the rapid development of insurance industry, the scale of insurance companies is expanding and the types of insurance are becoming diversified and dependent. Considering only one kind of insurance risk model can not meet the risk management needs of insurance companies. Therefore, it is necessary to combine multiple types of insurance to consider the risk situation of the insurance company, and the number of claims of the insurance company is often related to each other. Therefore, combined with the actual operation of the insurance company, It is of great significance to study the bankruptcy of the dependent multi-insurance model, not only to the management of insurance companies, but also to the supervision of supervision departments. For this reason, we consider a sparsely dependent risk model of double types of insurance: assume N1 (t) = N11 (t) N21 (t), N2 (t) = N22 (t) N12 (t), {N11 (t), t 0} as Poisson process with parameter 位 11, corresponding {N12 (t), T0} is a p1-sparse process of {N11 (t), t0}, {N22 (t), t0} is a Poisson process with a parameter 位 22, and the corresponding {N21 (t), t0} is a p2-sparse process of {N22 (t), t0}. The Poisson process {N 22 (t), t 0} and {N 11 (t), t 0} are independent of each other. Firstly, the two models are combined into one model, and the risk model of sparse dependence of claim number is established, and the general theory of ruin is studied, and the influence of sparsity on premium collection and ruin is also discussed. Secondly, the model is regarded as a two dimensional sparse dependent risk model, and the partial integro-differential equation of survival probability is obtained, and an iterative algorithm for calculating survival probability is given under the condition of exponential distribution.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：F224;F840.3

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