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随机最优控制在养老基金和微分对策论中的应用

摘要第4-6页
Abstract第6-7页
Chapter 1 Introduction第12-33页
    1.1 Introduction of Stochastic Control Theory第12-13页
    1.2 Introduction to Pension Funds第13-14页
    1.3 Preliminaries第14-18页
    1.4 Literature Review on Pension Funds第18-31页
        1.4.1 Stochastic Optimal control of DC pension funds第18-22页
        1.4.2 Viscosity solutions of the HJB equation第22-23页
        1.4.3 Optimal investment strategies in the presence of minimum guarantee第23-26页
        1.4.4 Stochastic optimal control of annuity contracts第26-31页
    1.5 Research Layout第31-32页
    1.6 Objectives of the Research第32-33页
Chapter 2 Stochastic Di?erential Equations (SDEs)第33-43页
    2.1 Brief Background of SDEs第33-34页
    2.2 General Representation of SDEs第34-35页
    2.3 Stochastic Di?erential Equations with Controls第35-42页
        2.3.1 Existence and Uniqueness of a Solution to a SDE第35-40页
        2.3.2 Dynamic Programming Principle第40-41页
        2.3.3 Hamilton Jacobi-Bellman Equation (HJB)第41-42页
    2.4 Summary第42-43页
Chapter 3 Stochastic Optimal Investment under Inflationary Market with Min-imum Guarantee for DC Pension Plans第43-61页
    3.1 Introduction第43-44页
    3.2 Proposed Financial Model第44-51页
        3.2.1 Salary第47页
        3.2.2 Contribution process第47-48页
        3.2.3 Minimum Guarantee第48-49页
        3.2.4 Wealth第49-51页
    3.3 Optimization Problem第51-54页
    3.4 Explicit Solution in CRRA Utility Case第54-57页
    3.5 Discussion of Problem第57-58页
    3.6 Summary第58-61页
Chapter 4 Modified Power Law Utility Function第61-73页
    4.1 Introduction第61-62页
    4.2 Problem Formulation第62-63页
        4.2.1 The Financial Market第62-63页
    4.3 Optimal Policy第63-66页
        4.3.1 Optimal Policy Before Retirement第63-64页
        4.3.2 Optimal Policy After Retirement第64-66页
    4.4 Proposed Power Law Utility第66-72页
        4.4.1 Optimal Policy Before Retirement第67-70页
        4.4.2 Optimal Policy After Retirement第70-72页
    4.5 Summary第72-73页
Chapter 5 Stochastic Di?erential Game第73-89页
    5.1 Introduction第73页
    5.2 Brief Literature on Game Theory第73-75页
    5.3 Problem Model第75-77页
        5.3.1 Conditions第76-77页
    5.4 Approach to Solution of Stochastic Optimal Controls第77-87页
        5.4.1 Iterative Optimal Control Estimates第84-87页
    5.5 Summary第87-89页
结论第89-91页
Conclusion and Future Work第91-94页
References第94-102页
List of Publications第102-104页
Acknowledgement第104-105页
Resume第105页

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