【摘要】：在保險(xiǎn)公司中，保費(fèi)定價(jià)（預(yù)測(cè)）是精算師的一個(gè)重要的任務(wù)。在制定保費(fèi)的過(guò)程中，精算師必須對(duì)多保單的風(fēng)險(xiǎn)進(jìn)行科學(xué)的分析和建模，從而制定合適的保費(fèi)。信度理論是保費(fèi)定價(jià)模型的一種主要的方法。在大部分的保費(fèi)定價(jià)模型中，常常假設(shè)風(fēng)險(xiǎn)之間相互獨(dú)立。這主要是基于簡(jiǎn)化數(shù)學(xué)模型的考慮。事實(shí)上，由于風(fēng)險(xiǎn)的復(fù)雜性，，風(fēng)險(xiǎn)之間常常呈現(xiàn)相依的情形。例如，研究表明，夫妻之間的壽命具有相依性，相鄰房屋之間可能面臨共同的火災(zāi)風(fēng)險(xiǎn)，同一個(gè)城市的居民面臨相同的地震風(fēng)險(xiǎn)等。 本文主要建立時(shí)間變化效應(yīng)相依和風(fēng)險(xiǎn)之間呈現(xiàn)某種相依情形下的信度模型。在某種相依結(jié)構(gòu)下，得到未來(lái)各年的保費(fèi)預(yù)測(cè)。并將該模型的方法運(yùn)用于GDP預(yù)測(cè)，得到較好的結(jié)論。 第二章利用信度理論方法研究了單合同和多合同下具有時(shí)間變化效應(yīng)的風(fēng)險(xiǎn)保費(fèi)的估計(jì)問(wèn)題。結(jié)論表明，具有時(shí)間變化效應(yīng)的信度模型,其信度估計(jì)仍然是個(gè)體索賠數(shù)據(jù)與聚合保費(fèi)的加權(quán)平均，且信度因子依賴(lài)時(shí)間變化效應(yīng)，從而推廣了經(jīng)典的信度原理。最后，將信度預(yù)測(cè)的方法運(yùn)用于中國(guó)GDP的預(yù)測(cè)問(wèn)題。若將不同的省份看成多個(gè)合同，不同年份的GDP數(shù)據(jù)看成各個(gè)合同在各年的索賠額（率），則我國(guó)各省的GDP數(shù)據(jù)恰吻合信度模型的數(shù)據(jù)結(jié)構(gòu)，我們?cè)跁r(shí)間變化效應(yīng)相依的信度模型中對(duì)2013及以后若干年的數(shù)據(jù)進(jìn)行信度預(yù)測(cè)，結(jié)果證明該預(yù)測(cè)方法有較高的精確度。 在第三章中討論了風(fēng)險(xiǎn)間相依下的信度模型。注意在經(jīng)典的Bu¨hlmann信度模型中，各個(gè)合同風(fēng)險(xiǎn)被假定為相互獨(dú)立的。本章假設(shè)保險(xiǎn)合同的風(fēng)險(xiǎn)之間存在相依性，我們建立了某種特殊相依結(jié)構(gòu)下的Bu¨hlmann信度模型和Bu¨hlmann-Straub信度模型，通過(guò)正交投影的方法分別得到對(duì)應(yīng)模型下的未來(lái)索賠的信度預(yù)測(cè)。結(jié)論表明，在保險(xiǎn)合同之間呈現(xiàn)這種相依結(jié)構(gòu)信度模型，其信度預(yù)測(cè)仍然是個(gè)體索賠數(shù)據(jù)與聚合保費(fèi)的加權(quán)和。
[Abstract]:In insurance companies, premium pricing (forecasting) is an important task for actuaries. In the process of making premium, the actuary must analyze and model the risk of multiple insurance policies scientifically, so as to make the appropriate premium. Reliability theory is a main method of premium pricing model. In most premium pricing models, risks are often assumed to be independent of each other. This is mainly based on the consideration of simplified mathematical models. In fact, because of the complexity of risk, risk often appears to be dependent on each other. For example, studies have shown that couples' lives depend on each other, that adjacent houses may face the same fire risk, and that residents of the same city may face the same earthquake risk. In this paper, we establish a reliability model in which there is a certain dependence between the time dependent and the risk. Under some dependent structure, the premium forecast for the next year is obtained. The model is applied to GDP prediction, and a good conclusion is obtained. In chapter 2, we use reliability theory to study the estimation of risk premium with time-varying effect under single contract and multi-contract. The results show that the reliability estimation of the reliability model with time-varying effect is still the weighted average of individual claim data and aggregate premium, and the reliability factor depends on the time-varying effect, thus generalizing the classical reliability principle. Finally, the reliability prediction method is applied to the prediction of GDP in China. If different provinces are regarded as multiple contracts, and the GDP data of different years are regarded as the claim amount (rate) of each contract in each year, the GDP data of each province in China coincide with the data structure of the reliability model. In the time-dependent reliability model, we predict the reliability of the data of 2013 and later years. The results show that the method has a high accuracy. In chapter 3, the reliability model of risk dependence is discussed. Note that in the classical Bu-hlmann reliability model, each contract risk is assumed to be independent of each other. In this chapter, assuming that the risks of insurance contracts depend on each other, we establish the Bu-hlmann reliability model and the Bu-hlmann-Straub reliability model under a special dependent structure. The reliability prediction of the future claims under the corresponding model is obtained by orthogonal projection The conclusion shows that the reliability prediction is still the weighted sum of individual claim data and aggregate premium.
【學(xué)位授予單位】：江西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F840.3;F224;O211.67

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 溫利民;龔海林;王靜龍;;具有風(fēng)險(xiǎn)相依結(jié)構(gòu)的B

本文編號(hào)：2148124