不确定性条件下动态投资组合管理研究
摘要
随着财富的积累和金融市场的完善，人们越来越希望能够通过金融市场和金融工具来改善和提高生活质量，这也就产生了对投资建议的需求。如何高效的管理投资组合已成为亟待解决的难题，而动态投资组合管理理论则为人们的投资实践提供了理论基础。
本文将研究动态投资组合问题，全文共分为六章。
第一章是诸论，第二章我们进行文献综述，总结不确定性下投资组合理论。在回顾Markowitz均值-方差模型的基础上，我们梳理现代资产组合选择理论的发展脉络，分析资产组合管理理论研究的最新进展。
第三章研究不确定性动态投资组合管理理论在实务工作中的运用，主要讨论证券投资基金和个人理财中的投资组合管理问题。
第四章我们研究随机收入对最优投资组合的影响。传统的默顿模型假定个人只有流动性强且易于交易的资产。但是，对于大部分家庭而言，其主要的资产是人力资本。首先我们在随机收入可以被完全对冲的情况下，研究随机收入对投资组合的影响。其次在不完全市场下，我们研究个体的最优投资／消费问题。
第五章中，我们在个体可以自由选择退休时间的情况下，研究具有常系数劳动收入率个体的最优退休和消费／投资问题。我们考虑了个体在退休前后风险偏好的变化，并假定在退休后的风险回避系数大于退休前，在CRRA效用函数假设下，我们利用鞅方法和变分不等式，获得了闭形式的最优策略，分析了时变效用函数对最优消费和投资的影响。
第六章我们研究工资收入者最优保险购买、消费和投资策略。为了对冲由于死亡导致的收入损失风险，个体通过向保险公司支付保费购买保险。我们的问题是个体如何决定最优的保险、消费／投资策略，以实现一生消费和终点财富所带来的总期望效用最大化，我们还在指数效用函数情况下获得显示解。
With the wealth aceumulation and the development of financial market,People areeagerly expecting to improve the living quality which creates the demand for financiaadvice.How to efficiently manage the portfolio becomes a problem that must be settled by us.Dynamic consumption and portfolio choice theory provides the investors a wonderfulframework for making decision.
This dissertation are concened dynamic consumption and portfolio choice problem,chieflydivided into six chapters.
Chapter 2 reviews the relevant literatures,aggregates portfolio theory.After reviewing theMarkowitz mean-variance model,we summarize the development of modern portfolioselection theory and elaborate the latest developments of portfolio management.
Chapter 3 we chiefly discuss the practice use of modern portfolio selection theory.ininvestment funds and personal finance
In Chapter four,we are concened the impact of random labor income to the optimalportfolio.Models in the Merton tradition assume that all wealth is held in a liquid,easily tradableform.However,the largest component of wealth for most households is human capital,.first wediscuss optimal investment and consumption problem when labor income is perfectly correlatedwith traded assets.secondly,we discuss optimal investment and consumption problem inincomplete market.
In Chapter five,We investigate an optimal portfolio,consumption and retirement decisionproblem in which an economic agent can determine the discretionary stopping time as a retirementtime with constant labor wage.We allow the preference of the agent to be changed before andafter retirement.It is assumed that the agent's coefficient of relative risk aversion becomes higherafter retirement..Under a constant relative risk aversion(CRRA)utility function,we obtain theoptimal policies in closed-forms using martingale methods and variational inequality methods.
In Chapter six,we set up a model to analyze the optimal consumption,life insurancepurchase and investment portfolio of a wage earner.In order to hedge the risk of losing incomestream by householder's unpredictable event,the household enters a life insurance contract bypaying a premium to an insurance company.The problem is to determine an optimalinsurance/investment/consumption strategy in order to maximize the expected total,discountedutility from consumption and terminal wealth.The case of exponential utilities is considered indetail to derive an explicit solution..
本文将研究动态投资组合问题，全文共分为六章。
第一章是诸论，第二章我们进行文献综述，总结不确定性下投资组合理论。在回顾Markowitz均值-方差模型的基础上，我们梳理现代资产组合选择理论的发展脉络，分析资产组合管理理论研究的最新进展。
第三章研究不确定性动态投资组合管理理论在实务工作中的运用，主要讨论证券投资基金和个人理财中的投资组合管理问题。
第四章我们研究随机收入对最优投资组合的影响。传统的默顿模型假定个人只有流动性强且易于交易的资产。但是，对于大部分家庭而言，其主要的资产是人力资本。首先我们在随机收入可以被完全对冲的情况下，研究随机收入对投资组合的影响。其次在不完全市场下，我们研究个体的最优投资／消费问题。
第五章中，我们在个体可以自由选择退休时间的情况下，研究具有常系数劳动收入率个体的最优退休和消费／投资问题。我们考虑了个体在退休前后风险偏好的变化，并假定在退休后的风险回避系数大于退休前，在CRRA效用函数假设下，我们利用鞅方法和变分不等式，获得了闭形式的最优策略，分析了时变效用函数对最优消费和投资的影响。
第六章我们研究工资收入者最优保险购买、消费和投资策略。为了对冲由于死亡导致的收入损失风险，个体通过向保险公司支付保费购买保险。我们的问题是个体如何决定最优的保险、消费／投资策略，以实现一生消费和终点财富所带来的总期望效用最大化，我们还在指数效用函数情况下获得显示解。
With the wealth aceumulation and the development of financial market,People areeagerly expecting to improve the living quality which creates the demand for financiaadvice.How to efficiently manage the portfolio becomes a problem that must be settled by us.Dynamic consumption and portfolio choice theory provides the investors a wonderfulframework for making decision.
This dissertation are concened dynamic consumption and portfolio choice problem,chieflydivided into six chapters.
Chapter 2 reviews the relevant literatures,aggregates portfolio theory.After reviewing theMarkowitz mean-variance model,we summarize the development of modern portfolioselection theory and elaborate the latest developments of portfolio management.
Chapter 3 we chiefly discuss the practice use of modern portfolio selection theory.ininvestment funds and personal finance
In Chapter four,we are concened the impact of random labor income to the optimalportfolio.Models in the Merton tradition assume that all wealth is held in a liquid,easily tradableform.However,the largest component of wealth for most households is human capital,.first wediscuss optimal investment and consumption problem when labor income is perfectly correlatedwith traded assets.secondly,we discuss optimal investment and consumption problem inincomplete market.
In Chapter five,We investigate an optimal portfolio,consumption and retirement decisionproblem in which an economic agent can determine the discretionary stopping time as a retirementtime with constant labor wage.We allow the preference of the agent to be changed before andafter retirement.It is assumed that the agent's coefficient of relative risk aversion becomes higherafter retirement..Under a constant relative risk aversion(CRRA)utility function,we obtain theoptimal policies in closed-forms using martingale methods and variational inequality methods.
In Chapter six,we set up a model to analyze the optimal consumption,life insurancepurchase and investment portfolio of a wage earner.In order to hedge the risk of losing incomestream by householder's unpredictable event,the household enters a life insurance contract bypaying a premium to an insurance company.The problem is to determine an optimalinsurance/investment/consumption strategy in order to maximize the expected total,discountedutility from consumption and terminal wealth.The case of exponential utilities is considered indetail to derive an explicit solution..
引文
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