复杂跳扩散风险模型中均值方差准则下的最优投资与最优再保险问题的研究
发布时间：2021-05-01 00:46
长期以来,风险控制与风险管理一直是保险公司和金融机构的一个重要课题.一方面,由于允许保险公司和金融机构在金融市场中进行投资,最优投资问题受到保险公司和金融机构的极大关注.另一方面,保险公司在开展再保险业务时,以减少潜在的利润为代价,将它的部分风险转移给另一方.再保业务过多会显著地降低利润,而再保业务过少即承担的风险过高则会导致偿付不足甚至引发破产.因此,如何选择合理的最优投资和再保险策略,在最大限度地提高收益的同时尽可能地降低风险,在金融和精算界得到了广泛的关注.相比于期望效用最大化准则,均值-方差准则能够使保险人或投资者在其可接受的收益下尽可能地降低风险（由收益的方差量化）.注意到,均值-方差准则不仅考虑了收益,同时还考虑了风险.由于其合理性以及实用性,均值-方差准则已成为金融理论中一种比较流行的风险度量工具,并得到了广泛的推广和应用.值得注意的是,由于缺乏期望迭代性（方差不满足可分性）,均值-方差准则不再满足Bellman最优性原理,这导致了动态不一致性的问题.对于随机最优控制问题中的动态不一致性问题,目前有两种方法处理:一是寻找最优的“预先承诺策略”;另一种方法是利用博弈论的理论...
【文章来源】：南京师范大学江苏省 211工程院校
【文章页数】：202 页
【学位级别】：博士
【文章目录】：
Abstract
摘要
Notation
Chapter 1 Introduction
1.1 Background
1.2 Literature review
1.2.1 Research based on different risk models
1.2.2 Research based on different criteria
1.3 Main contents and contribution
1.3.1 Main contents and research methods
1.3.2 Main contribution
Chapter 2 Preliminaries
2.1 Basic definitions and theorems
2.1.1 Poisson random measure
2.1.2 Ito formula
2.1.3 Markov chain
2.2 Mean-variance criterion
2.2.1 Classical mean-variance criterion
2.2.2 Mean-variance utility
Chapter 3 Optimal portfolio strategy with constraint on wealth underpartial information
3.1 Introduction
3.2 The model and the problem
3.3 The solution to the optimization problem
3.3.1 Some results in full information case
3.3.2 Optimal strategy under partial information
3.4 No shorting constraint
3.5 Conclusion
Chapter 4 Time-consistent portfolio selection in a Markovian regime-switchingmarket with common shock
4.1 Introduction
4.2 Model and problem formulation
4.2.1 Common shock model and assumption
4.2.2 Problem formulation
4.3 The solution to the optimization problem
4.4 Numerical analysis
4.5 Some results for n≥3
4.6 Conclusion
Chapter 5 Time-consistent reinsurance strategies for an insurer underthinning dependence
5.1 Introduction
5.2 The thinning dependence model of reinsurance
5.3 Problem formulation and the HJB equation
5.4 Time-consistent reinsurance strategies
5.4.1 The case of n＝2
5.4.2 The case of n≥3
5.5 Numerical analysis
5.6 Conclusion
Chapter 6 Optimal time-consistent reinsurance and investment strategyin a regime-switching economy with delayed system and common shock
6.1 Introduction
6.2 Common shock model of reinsurance and investment
6.3 Problem formulation and the HJB eqution
6.4 Time-consistent reinsurance and investment strategy
6.5 Numerical analysis
6.6 Conclusion
Chapter 7 Time-consistent reinsurance and investment strategies with on-ly risky assets
7.1 Introduction
7.2 Model and problem formulation
7.3 The solution to the optimization problem
7.4 Optimal results in some special cases
7.4.1 The case without jump
7.4.2 The case with a risk-free asset
7.5 Numerical analysis
7.6 Conclusion
Chapter 8 Conclusions and Prospects
8.1 Conclusions
8.2 Prospects
Bibliography
Publications or Finished Papers
Acknowledgements
本文编号：3169808
【文章来源】：南京师范大学江苏省 211工程院校
【文章页数】：202 页
【学位级别】：博士
【文章目录】：
Abstract
摘要
Notation
Chapter 1 Introduction
1.1 Background
1.2 Literature review
1.2.1 Research based on different risk models
1.2.2 Research based on different criteria
1.3 Main contents and contribution
1.3.1 Main contents and research methods
1.3.2 Main contribution
Chapter 2 Preliminaries
2.1 Basic definitions and theorems
2.1.1 Poisson random measure
2.1.2 Ito formula
2.1.3 Markov chain
2.2 Mean-variance criterion
2.2.1 Classical mean-variance criterion
2.2.2 Mean-variance utility
Chapter 3 Optimal portfolio strategy with constraint on wealth underpartial information
3.1 Introduction
3.2 The model and the problem
3.3 The solution to the optimization problem
3.3.1 Some results in full information case
3.3.2 Optimal strategy under partial information
3.4 No shorting constraint
3.5 Conclusion
Chapter 4 Time-consistent portfolio selection in a Markovian regime-switchingmarket with common shock
4.1 Introduction
4.2 Model and problem formulation
4.2.1 Common shock model and assumption
4.2.2 Problem formulation
4.3 The solution to the optimization problem
4.4 Numerical analysis
4.5 Some results for n≥3
4.6 Conclusion
Chapter 5 Time-consistent reinsurance strategies for an insurer underthinning dependence
5.1 Introduction
5.2 The thinning dependence model of reinsurance
5.3 Problem formulation and the HJB equation
5.4 Time-consistent reinsurance strategies
5.4.1 The case of n＝2
5.4.2 The case of n≥3
5.5 Numerical analysis
5.6 Conclusion
Chapter 6 Optimal time-consistent reinsurance and investment strategyin a regime-switching economy with delayed system and common shock
6.1 Introduction
6.2 Common shock model of reinsurance and investment
6.3 Problem formulation and the HJB eqution
6.4 Time-consistent reinsurance and investment strategy
6.5 Numerical analysis
6.6 Conclusion
Chapter 7 Time-consistent reinsurance and investment strategies with on-ly risky assets
7.1 Introduction
7.2 Model and problem formulation
7.3 The solution to the optimization problem
7.4 Optimal results in some special cases
7.4.1 The case without jump
7.4.2 The case with a risk-free asset
7.5 Numerical analysis
7.6 Conclusion
Chapter 8 Conclusions and Prospects
8.1 Conclusions
8.2 Prospects
Bibliography
Publications or Finished Papers
Acknowledgements
本文编号：3169808
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