【摘要】：面對(duì)一個(gè)問(wèn)題若碰到信息不精準(zhǔn)或缺失的情況,此時(shí)決策常常伴隨著風(fēng)險(xiǎn).由于不確定風(fēng)險(xiǎn)的客觀存可能導(dǎo)致潛在損失的發(fā)生,為了彌補(bǔ)損失,保險(xiǎn)行業(yè)應(yīng)運(yùn)而生.本文借助不確定理論這門(mén)新型的數(shù)學(xué)工具,用不確定刻畫(huà)風(fēng)險(xiǎn).本文第一部分介紹了不確定理論的定義,四個(gè)基本公理,不確定測(cè)度,不確定變量和不確定變量的分布的定義.具體給出了不確定變量的運(yùn)算法則.利用不確定過(guò)程及其獨(dú)立增量過(guò)程給出了極值定理.本文第二部分利用不確定更新過(guò)程和不確定索賠更新過(guò)程,給出了不確定風(fēng)險(xiǎn)模型的定義,定義了不確定風(fēng)險(xiǎn)模型的生存率.利用蓋伯的數(shù)學(xué)風(fēng)險(xiǎn)論導(dǎo)引中的最大損失總額的定義和不確定分布函數(shù)的定義以及不確定理論的極值定理求出不確定風(fēng)險(xiǎn)模型的生存率函數(shù).本文第三部分引入傳統(tǒng)的風(fēng)險(xiǎn)模型中帶折現(xiàn)率的離散時(shí)間破產(chǎn)模型到不確定理論中,本文利用不確定生存率的定義及定理,求出了帶折現(xiàn)率的不確定風(fēng)險(xiǎn)模型的生存率.姚凱應(yīng)用不確定分布的逆分布求出更改不確定風(fēng)險(xiǎn)模型的破產(chǎn)率,本文在這個(gè)更改的不確定風(fēng)險(xiǎn)模型下求出不確定生存率及其生存率函數(shù).并進(jìn)行了數(shù)據(jù)模擬.
[Abstract]:In the face of a problem where information is inaccurate or missing, decision-making is often accompanied by risk. Because the objective existence of uncertain risk may lead to the occurrence of potential loss, in order to make up for the loss, insurance industry emerges as the times require. In this paper, the uncertainty theory, a new mathematical tool, is used to describe the risk. The first part of this paper introduces the definition of uncertainty theory, four basic axioms, the definition of uncertainty measure, the definition of uncertain variable and the distribution of uncertain variable. The algorithm of uncertain variables is given in detail. The extreme value theorem is given by using the uncertain process and its independent incremental process. In the second part of this paper, the definition of the uncertain risk model and the survival rate of the uncertain risk model are given by using the uncertain renewal process and the uncertain claim renewal process. The survival rate function of uncertain risk model is obtained by using the definition of maximum total loss and the definition of uncertain distribution function and the extremum theorem of uncertainty theory in the guidance of mathematical risk theory. In the third part of this paper, the discrete-time ruin model with discount rate in the traditional risk model is introduced into the uncertainty theory. By using the definition and theorem of the uncertain survival rate, the survival rate of the uncertain risk model with discount rate is obtained. Yao Kai uses the inverse distribution of the uncertain distribution to calculate the failure rate of the modified uncertain risk model. In this paper, the uncertain survival rate and the survival rate function are obtained under this modified uncertain risk model. Data simulation is carried out.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211.67

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