本文選題：網(wǎng)絡(luò)馬氏骨架過程 + 復(fù)合網(wǎng)絡(luò)馬氏骨架過程��； 參考：《中國科學(xué)技術(shù)大學(xué)》2013年博士論文

【摘要】：網(wǎng)絡(luò)馬氏骨架過程是馬志明院士的科研團(tuán)隊近期提出的一類新過程,這是一個包含馬氏過程在內(nèi)的范圍很廣的過程類.這類過程非常適合模擬隨機(jī)變量之間的回歸型相依關(guān)系.本論文進(jìn)一步研究網(wǎng)絡(luò)馬氏骨架過程,并討論其在保險風(fēng)險中的應(yīng)用.首先引入復(fù)合網(wǎng)絡(luò)馬氏骨架過程的概念,并討論其極限性質(zhì).其次重點研究網(wǎng)絡(luò)馬氏骨架框架下總索賠量的精細(xì)大偏差和破產(chǎn)概率等問題. 直觀上來說,一個網(wǎng)絡(luò)馬氏骨架過程(web Markov skeleton process,簡記為WMSP)是一個純跳的馬氏骨架過程,并且跳間隔時間序列在給定其骨架信息的條件下是相互獨(dú)立的，一般地,一個WMSP的動態(tài)機(jī)制可以描述為如下形式：其中{Xn,n≥0}是馬爾科夫鏈,{Tn,n≥0}是跳間隔時間序列. 我們引入復(fù)合網(wǎng)絡(luò)馬氏骨架過程(compound web Markov skeleton process,簡記為CWMSP)它的機(jī)制可以描述如下：這里Nt表示到時間t為止跳躍的次數(shù),×是伴隨第i次跳躍的隨機(jī)變量. 由CWMSP描述的機(jī)制出現(xiàn)在許多自然和社會科學(xué)學(xué)科中,比如生物學(xué),金融,排隊論和保險等等,這里我們關(guān)注的是其在保險中的應(yīng)用.風(fēng)險的相依性是保險理論的研究熱點,也是難點.相對于更新風(fēng)險模型及其一般的拓廣模型,在保險理論中運(yùn)用網(wǎng)絡(luò)馬氏骨架過程來建模能夠充分的考慮歷史信息的相依性問題,這大大拓展了模型的適用性. 論文主要包含五個部分：第一部分是緒論和準(zhǔn)備知識部分,由第一章構(gòu)成,第二部分介紹網(wǎng)絡(luò)馬氏骨架過程并引入復(fù)合網(wǎng)絡(luò)馬氏骨架過程概念,給出了特定條件下復(fù)合網(wǎng)絡(luò)馬氏骨架過程的精細(xì)大偏差公式,這部分由第二章和第三章構(gòu)成.第三部分即第四章,給出了特定條件下總索賠量的精細(xì)大偏差公式.第五章到第七章,給出了一個特殊的復(fù)合網(wǎng)絡(luò)馬氏骨架過程,主要討論特定重災(zāi)風(fēng)險模型下的破產(chǎn)問題,包括有限時間破產(chǎn)概率,無限時間破產(chǎn)概率及破產(chǎn)概率的局部結(jié)果等問題.最后是總結(jié)和展望.
[Abstract]:The network Markov skeleton process is a new kind of process proposed recently by the research team of the academician of Ma Zhiming . This is a process class which contains Markov process . This kind of process is very suitable for simulating the regression model between random variables . This paper further studies the process of network Markov skeleton and discusses its application in insurance risk . Firstly , the concept of Markov skeleton process is introduced , and its limit properties are discussed .

intuitively , a network Markov process process , abbreviated as WMSP , is a pure - hop Markov skeleton process , and the time - hopping sequence is independent from each other given its skeleton information . Generally , a WMSP ' s dynamic mechanism can be described as the form where { X n , n & gt ; = 0 } is a Markov chain , { Tn , n & gt ; = 0 } is a time - hopping sequence .

We introduce a compound web Markov process process , which is abbreviated as CWMSP , and its mechanism can be described as follows : Here , the number of hops until time t is expressed , & # xd7 ; is a random variable with the ith jump .

The mechanism described by CWMSP occurs in many natural and social sciences disciplines , such as biology , finance , queuing theory , insurance , etc . We are concerned about the application of insurance theory . The dependence of risk is the research hotspot of insurance theory , and it is also a difficult point . Compared with updating risk model and its general topology model , using network Markov skeleton process in insurance theory can fully consider the dependency problem of historical information , which greatly expands the applicability of the model .

The paper mainly consists of five parts : the first part is the introduction and the preparation knowledge part , consists of the first chapter , the second part introduces the network Markov skeleton process and introduces the concept of the composite network Markov skeleton process , and gives the fine large deviation formula of the composite network Markov skeleton process under the special conditions . The fifth chapter , chapter four , gives a special composite network Markov skeleton process , which mainly discusses the problems of the bankruptcy under the specific gravity disaster risk model , including the limited time ruin probability , the infinite time ruin probability and the local result of the ruin probability .
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：F840.3;O211.62

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本文編號：1989061