最优投资策略选择和负风险模型相关课题研究
发布时间：2021-02-06 21:46
随着世界资本市场的高速增长,人们对投资组合策略选择问题越发关注。本文研究几类带有限制的投资组合选择问题以及负风险模型,这些问题在投资组合管理中具有深远的意义和广泛的适用性,该问题的解决为不同类型的投资者提供了相应的最优投资策略选择。第二章讨论了在要求财富过程不低于某一个基准财富过程的前提下,针对不同的个体效用函数如何来寻找最优投资策略的问题。这里我们把问题通过分解的方法加以研究,首先得到一组方程来求解拉格朗日乘子,进而得到最优的财富过程；然后利用投资组合来复制这个财富过程,从而得到最优的投资策略。最后我们利用蒙特卡罗模拟来表现该策略的效果。由于每个投资者的目标各式各样,我们在第三章研究带有个体消费的最优财富追踪模型,模型同时考虑了个体对消费以及财富效用的偏好。使用Hamilton-Jacobi-Bellman方法,我们求得投资策略的精确表达式,同时分析了所得到的解对个体偏好的敏感性。进一步,我们在第四章考虑了带有流动性限制的最优财富追踪问题。这个问题被公式化为最小化财富过程和期望财富过程间累积方差的有限制的最优投资组合选择问题。运用动态规划理论,整个问题变成求解带有流动性限制的HJB方...
【文章来源】：武汉大学湖北省 211工程院校 985工程院校 教育部直属院校
【文章页数】：99 页
【学位级别】：博士
【文章目录】：
摘要
Abstract
CONTENTS
Chapter 1 Introduction
1.1 Motivation and Literature Review
1.1.1 Portfolio management
1.1.2 Dual risk model
1.2 Preliminaries
1.2.1 Services objectives
1.2.2 Fundamental approach
1.3 The Summary of Main Results
1.3.1 Optimal portfolio selection strategies under some constraints
1.3.2 Optimal wealth tracking problem with consumption
1.3.3 Optimal portfolio on tracking the expected wealth process with liquidity constraints
1.3.4 Optimal constant barrier strategies in the dual risk model
1.4 Future Work
Chapter 2 Optimal Portfolio Selection Strategies under Some Constraints
2.1 Notations and Setting
2.2 Introduction and Statement of Results
2.3 Preliminary
2.3.1 Some main propositions
2.3.2 Simplifying the problem
2.4 Proof of Theorem 2.2.1
2.5 Simulations and Validation Study
Chapter 3 Optimal Wealth Tracking Problem with Consumption
3.1 Introduction and Statement of the Problem
3.2 Statement of the Results
3.3 Proofs of Theorems
3.4 The Sensitivity Analysis and Conclusion
Chapter 4 Optimal Portfolio on Tracking the Expected Wealth Process with Liquidity Constraints
4.1 Introduction and Statement of the Results
4.2 Solution of the Problem
4.2.1 The optimal strategy
4.2.2 Some remarks
4.3 Numerical Methods and Example
Chapter 5 Optimal Constant Barrier Strategies in the Dual Risk Model
5.1 The Dual Risk Model with the Compound Binomial Processes
5.1.1 Some main properties
5.1.2 The ruin probability and Lundbery Inequality
5.1.3 Further exact results
5.1.4 Example
5.2 Statement of the Main Problem and Preliminary
5.2.1 Notations and risk model
5.2.2 Integro-differential Equations with Boundary Conditions
i（u,b）and the Optimal Barrier Strategy in the Two State Makovian Environment"> 5.3 Expressions for Vi（u,b）and the Optimal Barrier Strategy in the Two State Makovian Environment
5.3.1 The case of exponential individual gains
5.3.2 The case of mixture of exponential individual gains
5.4 Numerical approximation and Examples
Bibliography
攻读博士学位期间论文发表（或待发表）情况
Acknowledgements
【参考文献】：
期刊论文
[1]相关负风险和模型的破产概率[J]. 董迎辉,王过京. 应用概率统计. 2004(03)
[2]完全离散二项风险模型下有限时间内的生存概率[J]. 龚日朝,杨向群. 应用概率统计. 2001(04)
本文编号：3021142
【文章来源】：武汉大学湖北省 211工程院校 985工程院校 教育部直属院校
【文章页数】：99 页
【学位级别】：博士
【文章目录】：
摘要
Abstract
CONTENTS
Chapter 1 Introduction
1.1 Motivation and Literature Review
1.1.1 Portfolio management
1.1.2 Dual risk model
1.2 Preliminaries
1.2.1 Services objectives
1.2.2 Fundamental approach
1.3 The Summary of Main Results
1.3.1 Optimal portfolio selection strategies under some constraints
1.3.2 Optimal wealth tracking problem with consumption
1.3.3 Optimal portfolio on tracking the expected wealth process with liquidity constraints
1.3.4 Optimal constant barrier strategies in the dual risk model
1.4 Future Work
Chapter 2 Optimal Portfolio Selection Strategies under Some Constraints
2.1 Notations and Setting
2.2 Introduction and Statement of Results
2.3 Preliminary
2.3.1 Some main propositions
2.3.2 Simplifying the problem
2.4 Proof of Theorem 2.2.1
2.5 Simulations and Validation Study
Chapter 3 Optimal Wealth Tracking Problem with Consumption
3.1 Introduction and Statement of the Problem
3.2 Statement of the Results
3.3 Proofs of Theorems
3.4 The Sensitivity Analysis and Conclusion
Chapter 4 Optimal Portfolio on Tracking the Expected Wealth Process with Liquidity Constraints
4.1 Introduction and Statement of the Results
4.2 Solution of the Problem
4.2.1 The optimal strategy
4.2.2 Some remarks
4.3 Numerical Methods and Example
Chapter 5 Optimal Constant Barrier Strategies in the Dual Risk Model
5.1 The Dual Risk Model with the Compound Binomial Processes
5.1.1 Some main properties
5.1.2 The ruin probability and Lundbery Inequality
5.1.3 Further exact results
5.1.4 Example
5.2 Statement of the Main Problem and Preliminary
5.2.1 Notations and risk model
5.2.2 Integro-differential Equations with Boundary Conditions
i（u,b）and the Optimal Barrier Strategy in the Two State Makovian Environment"> 5.3 Expressions for Vi（u,b）and the Optimal Barrier Strategy in the Two State Makovian Environment
5.3.1 The case of exponential individual gains
5.3.2 The case of mixture of exponential individual gains
5.4 Numerical approximation and Examples
Bibliography
攻读博士学位期间论文发表（或待发表）情况
Acknowledgements
【参考文献】：
期刊论文
[1]相关负风险和模型的破产概率[J]. 董迎辉,王过京. 应用概率统计. 2004(03)
[2]完全离散二项风险模型下有限时间内的生存概率[J]. 龚日朝,杨向群. 应用概率统计. 2001(04)
本文编号：3021142
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