本文選題：Poisson過程　切入點(diǎn)：復(fù)合Poisson-Geometric過程　出處：《南華大學(xué)》2014年碩士論文

【摘要】：風(fēng)險(xiǎn)理論是概率論與數(shù)理統(tǒng)計(jì)研究中的一個(gè)重要分支，也是精算數(shù)學(xué)研究的核心內(nèi)容，而破產(chǎn)理論又是風(fēng)險(xiǎn)理論的核心內(nèi)容。近年來，很多學(xué)者對經(jīng)典的風(fēng)險(xiǎn)模型進(jìn)行了推廣，，并取得一定成果。本文在已有成果基礎(chǔ)上做了進(jìn)一步研究，主要包括以下幾個(gè)方面： 第一、將經(jīng)典風(fēng)險(xiǎn)模型推廣為保費(fèi)收取為Poisson過程,賠償次數(shù)為二項(xiàng)過程的離散風(fēng)險(xiǎn)模型,用微分方法證明了調(diào)節(jié)系數(shù)的存在性，用矩母函數(shù)法推導(dǎo)出其破產(chǎn)概率表達(dá)式，且該表達(dá)式與經(jīng)典風(fēng)險(xiǎn)模型結(jié)論一致。 第二、推廣了保費(fèi)到達(dá)過程,考慮到風(fēng)險(xiǎn)事件與賠付事件不一定等價(jià)的實(shí)際情況，將理賠過程推廣為復(fù)合Poison-Geometric過程，并引入了隨機(jī)干擾項(xiàng)，建立了帶有干擾條件下多險(xiǎn)種風(fēng)險(xiǎn)模型，推廣了相關(guān)文獻(xiàn)的結(jié)論。 第三、將經(jīng)典風(fēng)險(xiǎn)模型推廣為保費(fèi)收取為Poison過程,索賠次數(shù)為復(fù)合Poison-Geometric過程的帶干擾風(fēng)險(xiǎn)模型，不僅研究了模型的破產(chǎn)概率，同時(shí)也得到了生存概率的一個(gè)積分微分方程，這些結(jié)論對保險(xiǎn)公司評估風(fēng)險(xiǎn)具有一定指導(dǎo)意義。
[Abstract]:Risk theory is an important branch of probability theory and mathematical statistics, and it is also the core content of actuarial mathematics research, and bankruptcy theory is the core content of risk theory.In recent years, many scholars have generalized the classical risk model and achieved some results.Based on the existing results, this paper makes further research, mainly including the following aspects:Firstly, the classical risk model is generalized to a discrete risk model in which the premium is collected as a Poisson process and the compensation is a binomial process. The existence of the adjustment coefficient is proved by differential method, and the ruin probability expression is derived by the moment generating function method.The expression is consistent with the conclusion of the classical risk model.Secondly, the premium arrival process is generalized, and considering the fact that the risk event and the indemnity event are not necessarily equivalent, the claim process is generalized to the compound Poison-Geometric process, and the stochastic disturbance term is introduced.The risk model of multiple types of insurance with interference is established, and the conclusion of relevant literature is extended.Thirdly, the classical risk model is extended to the Poison process with premium collection and the number of claims is the complex Poison-Geometric process. The ruin probability of the model is studied, and an integro-differential equation of survival probability is obtained.These conclusions have certain guiding significance for insurance companies to assess risk.
【學(xué)位授予單位】：南華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：O211.6;F840.3

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本文編號：1722065