橢圓分布的同單調(diào)性及其應(yīng)用
發(fā)布時(shí)間：2018-08-13 20:32
【摘要】：在傳統(tǒng)的風(fēng)險(xiǎn)理論中,一個投資組合的各個風(fēng)險(xiǎn)之間是被假定為相互獨(dú)立的.但是,一般來講,每個向量本身都有相依的成分.像在霧天里,同一地區(qū)的所有車輛被卷入事故里的概率都很大.在干燥的夏天,所有的木制房屋都更有可能發(fā)生火災(zāi).在相同地方,地震和火災(zāi)的索賠之間是相關(guān)的,盡管嚴(yán)格來講每個索賠不可預(yù)測.還有養(yǎng)老金,他們在同一個公司工作,乘坐相同的航班,那么這些人的死亡率在一定程度上是相依的.所以研究同單調(diào)對于更好的預(yù)測風(fēng)險(xiǎn)具有非常重要的現(xiàn)實(shí)意義.本文主要研究同單調(diào)和,共分五章.本文第一章是緒論,主要介紹了幾個具有相依性的現(xiàn)實(shí)例子,以及同單調(diào)研究的背景和意義.第二章第一部分主要介紹了分布函數(shù)、逆分布函數(shù)的定義以及相關(guān)性質(zhì)、定理,第二部分介紹了同單調(diào)性的概念以及相關(guān)定理.第三章第一部分介紹了同單調(diào)和的定義及相關(guān)定理,并舉出了幾個同單調(diào)和(積)的封閉性的例子,并且進(jìn)一步得出橢圓分布具有同單調(diào)和的封閉性,對數(shù)橢圓分布具有同單調(diào)積的封閉性.舉了一個離散的例子:幾何分布并不滿足同單調(diào)和的封閉性.因此得到結(jié)論,并不是所有分布都滿足同單調(diào)和(積)的封閉性.在第四章主要介紹了相關(guān)序的定義及幾個定理結(jié)果.第五章是總結(jié)及展望.
[Abstract]:In traditional risk theory, each risk of a portfolio is assumed to be independent of each other. Generally speaking, however, each vector itself has a dependent component. Like in foggy weather, all vehicles in the same area are likely to be involved in accidents. In dry summer, all wooden houses are more likely to fire. In the same place, there is a correlation between earthquake and fire claims, although each claim is strictly unpredictable. And pensions, where they work in the same company and take the same flights, their mortality rates are somewhat dependent. Therefore, the study of the same monotone is of great practical significance for better prediction of risk. This paper mainly studies the same monotone sum, which is divided into five chapters. The first chapter is an introduction, which mainly introduces several practical examples with dependence, and the background and significance of the same monotone research. The first part introduces the definition of distribution function, the definition of inverse distribution function and its related properties, theorems. The second part introduces the concept of homotonicity and related theorems. In chapter three, we introduce the definition of homomorphism and some related theorems, and give some examples of closure of homotonicity sum (product). Furthermore, we obtain that elliptic distribution has the closed property of homoharmonic. The logarithmic elliptic distribution has the closed property of the same monotone product. A discrete example is given: the geometric distribution does not satisfy the closed property of homoharmonic. Therefore, it is concluded that not all distributions satisfy the closure of the same monotone sum (product). In chapter 4, we mainly introduce the definition of related order and some theorems. The fifth chapter is the summary and prospect.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224
本文編號：2182104
[Abstract]:In traditional risk theory, each risk of a portfolio is assumed to be independent of each other. Generally speaking, however, each vector itself has a dependent component. Like in foggy weather, all vehicles in the same area are likely to be involved in accidents. In dry summer, all wooden houses are more likely to fire. In the same place, there is a correlation between earthquake and fire claims, although each claim is strictly unpredictable. And pensions, where they work in the same company and take the same flights, their mortality rates are somewhat dependent. Therefore, the study of the same monotone is of great practical significance for better prediction of risk. This paper mainly studies the same monotone sum, which is divided into five chapters. The first chapter is an introduction, which mainly introduces several practical examples with dependence, and the background and significance of the same monotone research. The first part introduces the definition of distribution function, the definition of inverse distribution function and its related properties, theorems. The second part introduces the concept of homotonicity and related theorems. In chapter three, we introduce the definition of homomorphism and some related theorems, and give some examples of closure of homotonicity sum (product). Furthermore, we obtain that elliptic distribution has the closed property of homoharmonic. The logarithmic elliptic distribution has the closed property of the same monotone product. A discrete example is given: the geometric distribution does not satisfy the closed property of homoharmonic. Therefore, it is concluded that not all distributions satisfy the closure of the same monotone sum (product). In chapter 4, we mainly introduce the definition of related order and some theorems. The fifth chapter is the summary and prospect.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224
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，本文編號：2182104
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