保險(xiǎn)公司的最優(yōu)投資再保險(xiǎn)策略問題一直是精算學(xué)研究中的熱點(diǎn)問題,也引起了金融保險(xiǎn)等業(yè)界部門的廣泛關(guān)注。本文主要從以下兩個(gè)方面討論了連續(xù)時(shí)間模型下的投資與再保險(xiǎn)優(yōu)化問題:（1）利用一種基于魯棒控制理論的方法來闡釋決策者的模糊厭惡態(tài)度是如何影響他的決策過程的;（2）建立嚴(yán)謹(jǐn)可行的數(shù)理金融模型來研究兩個(gè)不同決策者之間的交互影響。考慮到現(xiàn)有的文獻(xiàn)已經(jīng)證實(shí)了決策者不僅是風(fēng)險(xiǎn)厭惡的也是模糊厭惡的,本文將主要研究模型不確定性下的最優(yōu)化問題。我們假設(shè)決策者所考慮的模型由于參數(shù)估計(jì)存在錯(cuò)誤等原因,只是真實(shí)模型的一個(gè)近似。具體來講,決策者的金融投資模型以及索賠變化模型包含了擴(kuò)散模型或者跳模型中某些參數(shù)的不確定性。而且決策者需要通過求解一個(gè)最大最小問題,即最大化最壞情形下的表現(xiàn)泛函,來獲得穩(wěn)健的最優(yōu)策略。這個(gè)兩層的最優(yōu)化問題是一個(gè)與懲罰相關(guān)的多先驗(yàn)效應(yīng)模型,懲罰函數(shù)是由參考模型與備選模型之間的偏離程度通過相對(duì)熵的概念來構(gòu)建的。另一方面,我們討論了兩類決策者之間的交互影響。首先,我們考慮了兩個(gè)保險(xiǎn)公司之間的競(jìng)爭關(guān)系。關(guān)心競(jìng)爭對(duì)手的相對(duì)表現(xiàn)以及二者盈余過程的相關(guān)性導(dǎo)致了他們的控制策略相互影響。我們假設(shè)他們?cè)谙嗤?.. 

【文章來源】：華東師范大學(xué)上海市 211工程院校 985工程院校 教育部直屬院校

【文章頁數(shù)】：185 頁

【學(xué)位級(jí)別】：博士

【文章目錄】：
摘要
Abstract
Acknowledgements
Chapter 1 Introduction
    1.1 Literature Review
        1.1.1 Optimal Reinsurance Contracts
        1.1.2 Optimal Reinsurance and Investment Strategies
        1.1.3 Stochastic Differential Games
        1.1.4 Model Uncertainty
    1.2 Preliminaries
    1.3 Structure of the Thesis
    1.4 Comparison among the Incorporated Papers
Chapter 2 Robust Non-zero-sum Investment and Reinsurance Game with Default Risk
    2.1 Introduction
    2.2 The model formulation
    2.3 Solution to the robust non-zero-sum game
        2.3.1 The post-default case
        2.3.2 The pre-default case
        2.3.3 Verification theorem
    2.4 Special case: ANI case
    2.5 Numerical examples
    2.6 Conclusion
Chapter 3 Time-consistent Reinsurance-investment Games under Model Un-certainty
    3.1 Introduction
    3.2 Model formulation
    3.3 Nash equilibrium in compound Poisson risk model
    3.4 Nash equilibrium in diffusion approximated model
    3.5 Numerical examples
    3.6 Concluding remarks
Chapter 4 Robust Reinsurance Contracts with Mean-variance Criteria
    4.1 Introduction
    4.2 Problem formulation
    4.3 Solution to the robust reinsurance contract
        4.3.1 The insurer's problem
        4.3.2 The reinsurer's problem
    4.4 Utility loss of the suboptimal reinsurance and investment strategies
    4.5 Numerical examples
    4.6 Concluding remarks
Chapter 5 Concluding Remarks and Further Research
Appendix A Derivation of relative entropy in Chapter 2
Appendix B Proof of Lemma 2.3.1
Appendix C Proof of Corollary 2.4.1
Appendix D Derivation of relative entropy in Chapter 3
Appendix E Proof of Theorem 3.3.1
Appendix F Proof of Theorem 3.3.2
Bibliography
Publication List



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