网络马氏骨架过程框架下的保险风险研究

发布时间：2018-06-07 01:26

本文选题：网络马氏骨架过程 + 复合网络马氏骨架过程　；参考：《中国科学技术大学》2013年博士论文

【摘要】：网络马氏骨架过程是马志明院士的科研团队近期提出的一类新过程,这是一个包含马氏过程在内的范围很广的过程类.这类过程非常适合模拟随机变量之间的回归型相依关系.本论文进一步研究网络马氏骨架过程,并讨论其在保险风险中的应用.首先引入复合网络马氏骨架过程的概念,并讨论其极限性质.其次重点研究网络马氏骨架框架下总索赔量的精细大偏差和破产概率等问题. 直观上来说,一个网络马氏骨架过程(web Markov skeleton process,简记为WMSP)是一个纯跳的马氏骨架过程,并且跳间隔时间序列在给定其骨架信息的条件下是相互独立的，一般地,一个WMSP的动态机制可以描述为如下形式：其中{Xn,n≥0}是马尔科夫链,{Tn,n≥0}是跳间隔时间序列. 我们引入复合网络马氏骨架过程(compound web Markov skeleton process,简记为CWMSP)它的机制可以描述如下：这里Nt表示到时间t为止跳跃的次数,×是伴随第i次跳跃的随机变量. 由CWMSP描述的机制出现在许多自然和社会科学学科中,比如生物学,金融,排队论和保险等等,这里我们关注的是其在保险中的应用.风险的相依性是保险理论的研究热点,也是难点.相对于更新风险模型及其一般的拓广模型,在保险理论中运用网络马氏骨架过程来建模能够充分的考虑历史信息的相依性问题,这大大拓展了模型的适用性. 论文主要包含五个部分：第一部分是绪论和准备知识部分,由第一章构成,第二部分介绍网络马氏骨架过程并引入复合网络马氏骨架过程概念,给出了特定条件下复合网络马氏骨架过程的精细大偏差公式,这部分由第二章和第三章构成.第三部分即第四章,给出了特定条件下总索赔量的精细大偏差公式.第五章到第七章,给出了一个特殊的复合网络马氏骨架过程,主要讨论特定重灾风险模型下的破产问题,包括有限时间破产概率,无限时间破产概率及破产概率的局部结果等问题.最后是总结和展望.
[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 .
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F840.3;O211.62

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