本文關(guān)鍵詞： (a b)類分布 矩估計(jì) 極大似然估計(jì) 貝葉斯估計(jì)　出處：《吉林大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：從改革開放后的第一家保險(xiǎn)公司成立至今,保險(xiǎn)業(yè)飛速發(fā)展.如今的保險(xiǎn)業(yè)已覆蓋了衣食住行各個(gè)方面.AIG(American International Group,Inc.)是一個(gè)全球領(lǐng)先的保險(xiǎn)組織,AIG于今年提出了在保險(xiǎn)行業(yè)立身之本的四大要素,其中包括:成本的控制以及承保的盈利;利潤(rùn)的模式;多元文化的包容性;投資結(jié)構(gòu)的穩(wěn)健.由此看出AIG把承保的盈利作為第一條突出了條款理賠和利潤(rùn)的重要性.對(duì)于不同險(xiǎn)種的承保盈利,賠付率的估計(jì)是影響險(xiǎn)種定價(jià)以及公司利潤(rùn)的重要因素.其中索賠次數(shù)和索賠金額在厘定保費(fèi)中起最關(guān)鍵的作用,本文則是基于對(duì)索賠次數(shù)的分布進(jìn)行了更深的探索.一般來說,描述損失分布的常用方法有:幾何分布,二項(xiàng)分布,負(fù)二項(xiàng)分布,Poisson分布和正態(tài)分布.獲得損失分布的方法則有:經(jīng)典統(tǒng)計(jì)法,隨機(jī)模擬法和Bayes法.在實(shí)際的應(yīng)用中,保險(xiǎn)行業(yè)常用一些特殊的取值非負(fù)的計(jì)數(shù)隨機(jī)變量來刻畫損失次數(shù),這類特殊的損失次數(shù)是不屬于一般的損失分布的,所以針對(duì)不同的數(shù)據(jù)樣本確定不同的損失分布尤為關(guān)鍵.根據(jù)這一想法,本文考慮(a,b)類分布來刻畫損失次數(shù)的問題.從整體的角度,對(duì)(a,b)類分布進(jìn)行參數(shù)估計(jì),同時(shí)研究了該分布的方差與期望的關(guān)系.并給出了a與b的矩估計(jì)與極大似然估計(jì).在極大似然估計(jì)的基礎(chǔ)上,利用Lindley逼近引理,進(jìn)一步給出(a,b,0)類分布的貝葉斯估計(jì),最后運(yùn)用Matlab進(jìn)行蒙特卡洛模擬.從模擬結(jié)果中可看出,對(duì)于(a,b,0)類分布的估計(jì)中,若樣本數(shù)量足夠大,我們優(yōu)先選擇使用貝葉斯估計(jì),否則優(yōu)先選用矩估計(jì)較為合理。
[Abstract]:Since the establishment of the first insurance company after the reform and opening up, The insurance industry is booming. Today's insurance industry has covered all aspects of clothing, food, housing and transportation. AIGAmerican International Group Inc.is a leading global insurance organization that this year proposed four key elements for a foothold in the insurance industry. These include: cost control and underwriting profit; profit model; multiculturalism; The soundness of the investment structure shows that AIG regards underwritten profits as the first item highlighting the importance of clause settlement and profit. The estimation of the compensation rate is an important factor affecting the pricing of insurance and the profits of the company, in which the number of claims and the amount of the claim play the most important role in determining the premium. This paper is based on the distribution of the number of claims. Generally speaking, the commonly used methods to describe the distribution of losses are: geometric distribution, binomial distribution, The negative binomial distribution is Poisson distribution and normal distribution. The methods to obtain the loss distribution are classical statistical method, stochastic simulation method and Bayes method. In the insurance industry, some special non-negative counting random variables are used to describe the number of losses. Therefore, it is very important to determine the different loss distribution for different data samples. According to this idea, this paper considers the problem of describing the number of loss by using the class distribution. At the same time, the relationship between the variance and expectation of the distribution is studied, and the moment and maximum likelihood estimates of a and b are given. On the basis of the maximum likelihood estimation, the Bayesian estimation of the distribution of a and b is further given by using the Lindley approximation Lemma. Finally, Monte Carlo simulation is carried out by using Matlab. It can be seen from the simulation results that if the number of samples is large enough, we prefer Bayesian estimation, otherwise the moment estimation is more reasonable.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211.3

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本文編號(hào)：1508171