發(fā)布時(shí)間：2021-02-25 06:52

　　集體風(fēng)險(xiǎn)理論主要用來(lái)研究保險(xiǎn)公司的風(fēng)險(xiǎn)行為,百年來(lái)一直備受關(guān)注,是精算數(shù)學(xué)中重要的一支。其經(jīng)典模型由Lundberg在1903的論文（Lundberg（1903））中引進(jìn),而后經(jīng)過(guò)Harald Cramer等人的努力,使得模型在數(shù)學(xué)上的定義更為嚴(yán)謹(jǐn),被大多數(shù)人接受。經(jīng)典模型,同時(shí)也被稱(chēng)為Cramer-Lundberg風(fēng)險(xiǎn)模型,將所討論的公司模型刻畫(huà)為復(fù)合Poisson過(guò)程,在很多方面得到了應(yīng)用和發(fā)展。Gerber（1970）提出的帶干擾的復(fù)合Poisson模型和Andersen（1957）提出的更新模型,也就是Sparre Anderson模型就是其中比較有名的成功的例子。伴隨模型的發(fā)展和豐富,多種多樣的理論,方法和函數(shù)被引入風(fēng)險(xiǎn)理論的研究中。比如,更新理論,Winener-Hoff方程,It（?）公式,逐段決定馬氏過(guò)程還有鞅方法都是風(fēng)險(xiǎn)理論及其相關(guān)領(lǐng)域中比較常用的方法。Gerber and Shiu（1997,1998a）在古典模型中引入Gerber-Shiu罰金函數(shù),使得在精算中最重要三個(gè)變量,破產(chǎn)時(shí)間,破產(chǎn)赤字,破產(chǎn)前盈余,完美的統(tǒng)一在一起,之后由Tsai and Willmot... 

【文章來(lái)源】：南開(kāi)大學(xué)天津市 211工程院校 985工程院校 教育部直屬院校

【文章頁(yè)數(shù)】：108 頁(yè)

【學(xué)位級(jí)別】：博士

【文章目錄】：
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(φ_ij（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



本文編號(hào)：3050612