隨著世界資本市場(chǎng)的高速增長(zhǎng),人們對(duì)投資組合策略選擇問(wèn)題越發(fā)關(guān)注。本文研究幾類(lèi)帶有限制的投資組合選擇問(wèn)題以及負(fù)風(fēng)險(xiǎn)模型,這些問(wèn)題在投資組合管理中具有深遠(yuǎn)的意義和廣泛的適用性,該問(wèn)題的解決為不同類(lèi)型的投資者提供了相應(yīng)的最優(yōu)投資策略選擇。第二章討論了在要求財(cái)富過(guò)程不低于某一個(gè)基準(zhǔn)財(cái)富過(guò)程的前提下,針對(duì)不同的個(gè)體效用函數(shù)如何來(lái)尋找最優(yōu)投資策略的問(wèn)題。這里我們把問(wèn)題通過(guò)分解的方法加以研究,首先得到一組方程來(lái)求解拉格朗日乘子,進(jìn)而得到最優(yōu)的財(cái)富過(guò)程；然后利用投資組合來(lái)復(fù)制這個(gè)財(cái)富過(guò)程,從而得到最優(yōu)的投資策略。最后我們利用蒙特卡羅模擬來(lái)表現(xiàn)該策略的效果。由于每個(gè)投資者的目標(biāo)各式各樣,我們?cè)诘谌卵芯繋в袀�(gè)體消費(fèi)的最優(yōu)財(cái)富追蹤模型,模型同時(shí)考慮了個(gè)體對(duì)消費(fèi)以及財(cái)富效用的偏好。使用Hamilton-Jacobi-Bellman方法,我們求得投資策略的精確表達(dá)式,同時(shí)分析了所得到的解對(duì)個(gè)體偏好的敏感性。進(jìn)一步,我們?cè)诘谒恼驴紤]了帶有流動(dòng)性限制的最優(yōu)財(cái)富追蹤問(wèn)題。這個(gè)問(wèn)題被公式化為最小化財(cái)富過(guò)程和期望財(cái)富過(guò)程間累積方差的有限制的最優(yōu)投資組合選擇問(wèn)題。運(yùn)用動(dòng)態(tài)規(guī)劃理論,整個(gè)問(wèn)題變成求解帶有流動(dòng)性限制的HJB方... 

【文章來(lái)源】：武漢大學(xué)湖北省 211工程院校 985工程院校 教育部直屬院校

【文章頁(yè)數(shù)】：99 頁(yè)

【學(xué)位級(jí)別】：博士

【文章目錄】：
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 V_i（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
攻讀博士學(xué)位期間論文發(fā)表（或待發(fā)表）情況
Acknowledgements


【參考文獻(xiàn)】：
期刊論文
[1]相關(guān)負(fù)風(fēng)險(xiǎn)和模型的破產(chǎn)概率[J]. 董迎輝,王過(guò)京.  應(yīng)用概率統(tǒng)計(jì). 2004(03)
[2]完全離散二項(xiàng)風(fēng)險(xiǎn)模型下有限時(shí)間內(nèi)的生存概率[J]. 龔日朝,楊向群.  應(yīng)用概率統(tǒng)計(jì). 2001(04)



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