跳扩散模型在风险理论中的应用
发布时间：2021-02-25 06:52
集体风险理论主要用来研究保险公司的风险行为,百年来一直备受关注,是精算数学中重要的一支。其经典模型由Lundberg在1903的论文（Lundberg（1903））中引进,而后经过Harald Cramer等人的努力,使得模型在数学上的定义更为严谨,被大多数人接受。经典模型,同时也被称为Cramer-Lundberg风险模型,将所讨论的公司模型刻画为复合Poisson过程,在很多方面得到了应用和发展。Gerber（1970）提出的带干扰的复合Poisson模型和Andersen（1957）提出的更新模型,也就是Sparre Anderson模型就是其中比较有名的成功的例子。伴随模型的发展和丰富,多种多样的理论,方法和函数被引入风险理论的研究中。比如,更新理论,Winener-Hoff方程,It（?）公式,逐段决定马氏过程还有鞅方法都是风险理论及其相关领域中比较常用的方法。Gerber and Shiu（1997,1998a）在古典模型中引入Gerber-Shiu罚金函数,使得在精算中最重要三个变量,破产时间,破产赤字,破产前盈余,完美的统一在一起,之后由Tsai and Willmot...
【文章来源】：南开大学天津市 211工程院校 985工程院校 教育部直属院校
【文章页数】：108 页
【学位级别】：博士
【文章目录】：
Abstract
摘要
1 Introduction
1.1 Background
1.2 Organization and Main Contents of This Thesis
2 Perturbed compound Poisson risk model with a threshold dividend strategy
2.1 Introduction
2.2 Preliminaries
2.2.1 The related process
2.2.2 The solution to defective IDE
2.3 Integro-differential Equations for the Gerber-Shiu function
2.4 Integro-differential Equations for the expected discounted dividend payments function
2.5 Conclusions
3 The dividend function in the jump-diffusion dual model with barrier dividend strategy
3.1 Introduction
3.2 Preliminaries
3.3 Integro-differential Equations and their Solution
3.4 Example
4 Study of Markov-modulated jump-diffusion risk process
4.1 A renewal jump-diffusion process
4.1.1 Risk process analyzed as fluid flow
4.1.2 Fundamental quantities of（R（s）,J（s））
4.2 Markov-modulated jump-diffusion process
4.2.1 The generalization of fluid flow（R（s）,J（s））
4.2.2 Back to the risk process
4.2.3 Passage times of the Markov-modulated process
0,U（Υ0-）,U（Υ0））"> 4.2.4 The joint distribution of（Υ0,U（Υ0-）,U（Υ0））
4.2.5 Example
4.3 Markov-modulated jump-diffusion process with the presence of threshold dividend
4.3.1 The auxiliary vector V（u,b）
ij（u,b）)"> 4.3.2 The auxiliary matrix(φij（u,b）)
4.3.3 Main results
4.3.4 Examples
4.4 Markov-modulated jump-diffusion process with multi-layer dividend strategy
4.4.1 Risk model with multi-layer dividend
4.4.2 Main results
4.4.3 Example
Bibliography
Acknowledgements
Resume and Publications
本文编号：3050612
【文章来源】：南开大学天津市 211工程院校 985工程院校 教育部直属院校
【文章页数】：108 页
【学位级别】：博士
【文章目录】：
Abstract
摘要
1 Introduction
1.1 Background
1.2 Organization and Main Contents of This Thesis
2 Perturbed compound Poisson risk model with a threshold dividend strategy
2.1 Introduction
2.2 Preliminaries
2.2.1 The related process
2.2.2 The solution to defective IDE
2.3 Integro-differential Equations for the Gerber-Shiu function
2.4 Integro-differential Equations for the expected discounted dividend payments function
2.5 Conclusions
3 The dividend function in the jump-diffusion dual model with barrier dividend strategy
3.1 Introduction
3.2 Preliminaries
3.3 Integro-differential Equations and their Solution
3.4 Example
4 Study of Markov-modulated jump-diffusion risk process
4.1 A renewal jump-diffusion process
4.1.1 Risk process analyzed as fluid flow
4.1.2 Fundamental quantities of（R（s）,J（s））
4.2 Markov-modulated jump-diffusion process
4.2.1 The generalization of fluid flow（R（s）,J（s））
4.2.2 Back to the risk process
4.2.3 Passage times of the Markov-modulated process
0,U（Υ0-）,U（Υ0））"> 4.2.4 The joint distribution of（Υ0,U（Υ0-）,U（Υ0））
4.2.5 Example
4.3 Markov-modulated jump-diffusion process with the presence of threshold dividend
4.3.1 The auxiliary vector V（u,b）
ij（u,b）)"> 4.3.2 The auxiliary matrix(φij（u,b）)
4.3.3 Main results
4.3.4 Examples
4.4 Markov-modulated jump-diffusion process with multi-layer dividend strategy
4.4.1 Risk model with multi-layer dividend
4.4.2 Main results
4.4.3 Example
Bibliography
Acknowledgements
Resume and Publications
本文编号：3050612
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