【摘要】：破產(chǎn)概率是現(xiàn)代保險(xiǎn)精算學(xué)中的一個(gè)經(jīng)典問題,主要是研究保險(xiǎn)公司發(fā)生大額索賠時(shí)在有限時(shí)間內(nèi)的生存概率或者破產(chǎn)概率.唐啟鶴和汪世界是現(xiàn)代保險(xiǎn)精算理論的代表人物,他們將破產(chǎn)概率的研究推廣到了一個(gè)新的高度. 但是,我們發(fā)現(xiàn)幾乎所有文章研究的都是一種索賠,也就是說(shuō)保險(xiǎn)公司僅提供了一種保單的業(yè)務(wù).事實(shí)上這個(gè)假設(shè)是不正確的,多維風(fēng)險(xiǎn)模型的破產(chǎn)概率問題更接近保險(xiǎn)公司的實(shí)際情況.因此,本文考慮有多種保單的多維風(fēng)險(xiǎn)模型. 在本文中,假設(shè)保險(xiǎn)公司有8種保單,第i種保單的凈損失記為{Xi,Xiκ,κ≥1},它們是一列獨(dú)立同分布的隨機(jī)變量,第κ年的利率記為rκ,κ=1,2,…,{Xi,Xiκ,κ≥1}si=1和{rκ,κ=1,2,…}是相互獨(dú)立的,我們得出了帶有隨機(jī)利率的離散時(shí)間多維風(fēng)險(xiǎn)模型的有限時(shí)間破產(chǎn)概率的漸近性.
[Abstract]:Ruin probability is a classical problem in modern insurance actuary. It mainly studies the survival probability or ruin probability of insurance company in a limited time when a large claim is made. Tang Qi-he and Wang World are representatives of modern actuarial theory of insurance. They extend the study of bankruptcy probability to a new height. However, we find that almost all of the articles are concerned with a claim, that is, the insurance company provides only one kind of insurance policy business. In fact, this assumption is incorrect. The ruin probability problem of multidimensional risk model is closer to the actual situation of insurance company. Therefore, this paper considers multidimensional risk models with multiple policies. In this paper, assuming the insurance company has eight policies, the net loss of the first type of policy is recorded as {Xi,Xi 魏, 魏 鈮，

本文編號(hào)：2383673