模型不确定性及博弈框架下最优投资与再保险策略的相关研究
发布时间：2021-10-31 17:21
保险公司的最优投资再保险策略问题一直是精算学研究中的热点问题,也引起了金融保险等业界部门的广泛关注。本文主要从以下两个方面讨论了连续时间模型下的投资与再保险优化问题:（1）利用一种基于鲁棒控制理论的方法来阐释决策者的模糊厌恶态度是如何影响他的决策过程的;（2）建立严谨可行的数理金融模型来研究两个不同决策者之间的交互影响。考虑到现有的文献已经证实了决策者不仅是风险厌恶的也是模糊厌恶的,本文将主要研究模型不确定性下的最优化问题。我们假设决策者所考虑的模型由于参数估计存在错误等原因,只是真实模型的一个近似。具体来讲,决策者的金融投资模型以及索赔变化模型包含了扩散模型或者跳模型中某些参数的不确定性。而且决策者需要通过求解一个最大最小问题,即最大化最坏情形下的表现泛函,来获得稳健的最优策略。这个两层的最优化问题是一个与惩罚相关的多先验效应模型,惩罚函数是由参考模型与备选模型之间的偏离程度通过相对熵的概念来构建的。另一方面,我们讨论了两类决策者之间的交互影响。首先,我们考虑了两个保险公司之间的竞争关系。关心竞争对手的相对表现以及二者盈余过程的相关性导致了他们的控制策略相互影响。我们假设他们在相同的...
【文章来源】：华东师范大学上海市 211工程院校 985工程院校 教育部直属院校
【文章页数】：185 页
【学位级别】：博士
【文章目录】：
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
本文编号：3468541
【文章来源】：华东师范大学上海市 211工程院校 985工程院校 教育部直属院校
【文章页数】：185 页
【学位级别】：博士
【文章目录】：
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
本文编号：3468541
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