本文選題：生存概率　切入點(diǎn)：預(yù)警區(qū)　出處：《延安大學(xué)》2017年碩士論文

【摘要】：結(jié)合當(dāng)前金融保險(xiǎn)行業(yè)實(shí)際,考慮到再投資、隨機(jī)干擾及保費(fèi)的收取為復(fù)合過(guò)程,同時(shí)考慮到在保險(xiǎn)事務(wù)中,風(fēng)險(xiǎn)事件和理賠事件有可能不等價(jià)的事實(shí),特別是保險(xiǎn)公司推出免賠額和無(wú)賠款折扣等制度.現(xiàn)對(duì)毛澤春等提出的復(fù)合Poisson-Geometric風(fēng)險(xiǎn)模型做進(jìn)一步推廣,使其更接近保險(xiǎn)公司的實(shí)際經(jīng)營(yíng)運(yùn)作,并對(duì)修正的復(fù)合風(fēng)險(xiǎn)模型的精算量進(jìn)行研究.全文的主要研究成果如下:首先,建立保費(fèi)收入服從復(fù)合負(fù)二項(xiàng)分布,理賠服從復(fù)合Poisson-Geometric過(guò)程的帶投資的干擾風(fēng)險(xiǎn)模型.通過(guò)對(duì)盈余過(guò)程性質(zhì)的研究,得到了最終破產(chǎn)概率公式和破產(chǎn)概率上界的Lundberg不等式.以及利用鞅知識(shí)對(duì)其盈余首次達(dá)到給定水平的時(shí)刻進(jìn)行研究,得到了給定水平時(shí)刻的拉氏變換以及相應(yīng)的期望、方差和3階中心矩的具體表達(dá)式.其次,在第三章風(fēng)險(xiǎn)模型的基礎(chǔ)上,假設(shè)保費(fèi)收入服從復(fù)合Poisson過(guò)程.利用全期望公式對(duì)修正的復(fù)合Poisson-Geometric風(fēng)險(xiǎn)模型的生存概率、Gerber-Shiu折現(xiàn)懲罰函數(shù)以及預(yù)警區(qū)問(wèn)題進(jìn)行研究,推導(dǎo)出了所滿足的積分微分方程.最后,在第四章建立的風(fēng)險(xiǎn)模型的基礎(chǔ)上,引入紅利邊界.利用全期望公式和盈余過(guò)程的馬氏性,得到了直至破產(chǎn)時(shí)總紅利現(xiàn)值的期望、矩母函數(shù)及其n階矩所滿足的積分微分方程.
[Abstract]:Considering the reality of the current financial and insurance industry, considering that reinvestment, random interference and premium collection are composite processes, and considering the fact that risk events and claims events may not be equivalent in insurance affairs, In particular, insurance companies have introduced deductible and non-indemnity discount systems. Now the composite Poisson-Geometric risk model proposed by Mao Zechun and others has been further extended to make it closer to the actual operation of the insurance company. The main results of this paper are as follows: firstly, the negative binomial distribution of premium income is established. Compensation claims from the composite Poisson-Geometric process with the investment risk model. Through the study of the nature of the earnings process, The final ruin probability formula and the Lundberg inequality of the upper bound of the ruin probability are obtained. The Lagrangian transformation at the given level and the corresponding expectation are obtained by using martingale knowledge to study the moment at which the surplus reaches a given level for the first time. The concrete expressions of variance and third-order central moments. Secondly, on the basis of the risk model in Chapter 3, Assuming that premium income is derived from the compound Poisson process, the survival probability of the modified compound Poisson-Geometric risk model is studied by using the full expectation formula and the problem of the discounted penalty function of Gerber-Shiu and the early warning area is studied. Finally, the satisfied integrodifferential equation is derived. On the basis of the risk model established in Chapter 4, the dividend boundary is introduced. By using the full expectation formula and the Markov property of the surplus process, the expectation of the present value of the total dividend, the moment generating function and its n-order moments are obtained.
【學(xué)位授予單位】：延安大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O211.67

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 賀麗娟;王成勇;張鍇;;變保費(fèi)率復(fù)合Poisson-Geometric過(guò)程風(fēng)險(xiǎn)模型的Gerber-Shiu折現(xiàn)懲罰函數(shù)[J];工程數(shù)學(xué)學(xué)報(bào);2016年02期

2 魏龍飛;;具有相依結(jié)構(gòu)離散時(shí)間模型破產(chǎn)概率的上界[J];經(jīng)濟(jì)數(shù)學(xué);2016年01期

3 張媛媛;王文勝;;帶常利率的擾動(dòng)復(fù)合泊松風(fēng)險(xiǎn)模型（英文）[J];應(yīng)用概率統(tǒng)計(jì);2015年04期

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本文編號(hào)：1689463