本文選題：復(fù)合馬爾可夫二項模型 + Gerber-Shiu罰金函數(shù)��； 參考：《湘潭大學(xué)》2013年碩士論文

【摘要】：在過去很長一段時間,關(guān)于保險公司紅利策略的研究主要集中于連續(xù)時間模型,而離散時間模型中紅利策略的研究也有其研究價值.在以往的離散時間模型研究中,主要以復(fù)合二項模型為主,但它的主要缺陷是假設(shè)保險公司索賠的發(fā)生是相互獨立的,這與現(xiàn)實是相悖的.在我們生活的現(xiàn)實世界中,由于可能引發(fā)風(fēng)險業(yè)務(wù)的共同因素存在,所以在本文中我們假設(shè)任意時刻索賠的發(fā)生與否都與它前一時刻的索賠情況有關(guān),從而引入一個復(fù)合馬爾可夫二項模型,它可以看成是復(fù)合二項模型的推廣,在此模型中我們考慮幾種紅利的支付策略. 第一章緒論部分介紹與本文內(nèi)容相關(guān)的研究背景和研究現(xiàn)狀,以及本文選題的意義. 第二章主要討論復(fù)合馬爾可夫二項模型,并在該模型中引進(jìn)一個常數(shù)紅利邊界策略,得到了Gerber-Shiu罰金函數(shù)所滿足的線性方程組,且證得該方程組存在唯一解.最后,作為罰金函數(shù)的一些應(yīng)用實例我們給出了一些具體風(fēng)險量的計算公式. 在第三章中,我們在復(fù)合馬爾可夫二項模型中考慮常紅利邊界策略下的紅利期望現(xiàn)值,得到了紅利期望現(xiàn)值所滿足的方程組,且在相對寬松的條件下,求解出了直到破產(chǎn)發(fā)生時紅利期望現(xiàn)值的近似解. 在第四章中,我們在復(fù)合馬爾可夫二項模型中引進(jìn)隨機(jī)支付紅利的策略,并在此策略下討論Gerber-Shiu罰金函數(shù).我們得到了罰金函數(shù)所滿足的線性方程組、遞推公式.作為罰金函數(shù)的特例,我們同樣討論了一些具體的風(fēng)險量,并給出了相應(yīng)結(jié)論.
[Abstract]:In the past a long time, the research on dividend strategy of insurance company is mainly focused on the continuous time model, and the dividend strategy in the discrete time model also has its research value. In the previous study of discrete time model, the compound binomial model is the main one, but its main defect is to assume that the claim of insurance company is independent of each other, which is contrary to the reality. In the real world where we live, because there are common factors that can trigger a risky business, in this paper we assume that the claim at any moment is related to the claim at the previous moment. Therefore, a compound Markov binomial model is introduced, which can be regarded as a generalization of the compound binomial model. In this model, we consider several dividend payment strategies. The first chapter introduces the research background and research status related to the content of this paper, as well as the significance of this topic. In the second chapter, we mainly discuss the compound Markov binomial model, and introduce a constant dividend boundary strategy in the model. We obtain the system of linear equations satisfied by the Gerber-Shiu penalty function, and prove the existence and unique solution of the system. Finally, as some application examples of the penalty function, we give some formulas for calculating the specific risk. In the third chapter, we consider the expected present value of dividend under the constant dividend boundary strategy in the compound Markov binomial model, and obtain the equations satisfying the expected present value of dividend, and under relatively loose conditions, An approximate solution to the expected present value of the dividend until the time of bankruptcy is obtained. In chapter 4, we introduce the strategy of random dividend payment in the compound Markov binomial model, and discuss the Gerber-Shiu penalty function under this strategy. We obtain the system of linear equations and the recurrence formula of the fine function. As a special case of penalty function, we also discuss some specific risk quantities and give corresponding conclusions.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.3;F224;O211.62

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