一种为提前退休计划筹集资金的组合投资策略
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摘要
组合投资优化理论是现代金融投资理论的重要组成部分,亦是金融学中的重要研究课题之一,其目的是寻求一个在给定收益水平下使投资风险最小化,或者在给定的投资风险水平下使投资收益最大化的最优投资组合。它主要运用凸分析、随机分析、非光滑优化、(非)线性规划等数学工具,并与现代投资组合理论的基本方法相结合,通过建立数学模型定量的讨论金融市场的投资规律并为个人或机构投资者提供理论指导。
本文主要研究金融领域中的组合投资策略在为提前退休计划筹集资金这一实际问题领域中的应用,提出了一类基于债券和储蓄的组合投资策略,建立了固定收益模型,风险收益模型以及基于风险收益的连续投资模型,并详细介绍了单纯形法的求解原理和计算步骤,进而给出了该类组合投资模型基本可行解的确立方法,实现了用单纯形法对此类模型的求解。
文中提出的组合投资模型均为线性模型,其中连续投资模型不同于以往证券组合投资中的连续单周期投资模型和多周期投资模型,采用了逐年连续追加投资的理念,推导出了新的约束条件,进而进行了模型求解和分析。此外,本文针对一实际的为提前退休计划筹集资金问题,运用各模型进行定量求解,然后通过对比分析给出了合理的投资建议,具有一定的实际指导意义。需要说明的是,虽然连续投资模型并没有在这一实际问题中体现出自身的优势,但是通过对比明显可以看出它的确要优于前两种模型,而这一点对于大型投资计划而言则可能具有一定的指导意义。
本文并未考虑交易费用等对组合投资的影响,未来可以根据实际情况,加入交易费用以及加入各种证券,比如股票,基金等共同参与投资,并利用不同的风险度量准则以期制定出更优的组合投资策略。
Theory of portfolio optimization is an important part of the modern finance investment theories; it is also one of the important research content in economics which aims to attain the portfolios of the maximum investment's return with the given value of the risk or of the minimum investment's risk with the given level of the investment's return. It mainly uses mathematical facilities such as convex analysis, random analysis, non-smooth analysis, (nonlinear) linear programming etc, combined with the basic method of modem portfolio theory. By setting up mathematical models, it discusses the investment rules of finance market and offers theoretic guide for investors.
This text mainly studies the portfolio strategy within financial realm for actual problems concerning raising the funds for early retirement plans. It puts forward a portfolio strategy based on bonds and savings. Then, it sets up three mathematical models: the fixed income model, the floating income model and the continuous investment model based on floating income. Furthermore, it goes into detail the basic principle and the calculation steps of the simplex algorithm. In addition, it puts forward a method about finding out a basic feasible solution in order to use the simplex algorithm to solve this kind of models.
All of the mathematical models put forward in the text are linear models. However, the continuous investment model differs from the continuous single period's investment models or the several periods' investment models within stock certificate's portfolio realm. It adopts the method of continuous supplemental investment year by year and deduces new constraints, then solves and analyzes the model. In addition, the article aims at an actual problem concerning raising the funds for early retirement plans, solving each model quantificational, then analyzes through a contrast and gives a reasonable investment suggestion which is useful in actually. However, the continuous investment model has not display advantage in this actually problem, it may surpass the other models and have better applied foreground for large investment plans.
In this article, it doesn't consider the influence of the factors, such as trade tax etc, upon the portfolio strategy. Therefore, it can join trade tax and join various stock certificates, for example, stocks, funds etc, into the portfolio strategy in the future, it can also make use of the different risk norms to draw up a more excellent strategy.
本文主要研究金融领域中的组合投资策略在为提前退休计划筹集资金这一实际问题领域中的应用,提出了一类基于债券和储蓄的组合投资策略,建立了固定收益模型,风险收益模型以及基于风险收益的连续投资模型,并详细介绍了单纯形法的求解原理和计算步骤,进而给出了该类组合投资模型基本可行解的确立方法,实现了用单纯形法对此类模型的求解。
文中提出的组合投资模型均为线性模型,其中连续投资模型不同于以往证券组合投资中的连续单周期投资模型和多周期投资模型,采用了逐年连续追加投资的理念,推导出了新的约束条件,进而进行了模型求解和分析。此外,本文针对一实际的为提前退休计划筹集资金问题,运用各模型进行定量求解,然后通过对比分析给出了合理的投资建议,具有一定的实际指导意义。需要说明的是,虽然连续投资模型并没有在这一实际问题中体现出自身的优势,但是通过对比明显可以看出它的确要优于前两种模型,而这一点对于大型投资计划而言则可能具有一定的指导意义。
本文并未考虑交易费用等对组合投资的影响,未来可以根据实际情况,加入交易费用以及加入各种证券,比如股票,基金等共同参与投资,并利用不同的风险度量准则以期制定出更优的组合投资策略。
Theory of portfolio optimization is an important part of the modern finance investment theories; it is also one of the important research content in economics which aims to attain the portfolios of the maximum investment's return with the given value of the risk or of the minimum investment's risk with the given level of the investment's return. It mainly uses mathematical facilities such as convex analysis, random analysis, non-smooth analysis, (nonlinear) linear programming etc, combined with the basic method of modem portfolio theory. By setting up mathematical models, it discusses the investment rules of finance market and offers theoretic guide for investors.
This text mainly studies the portfolio strategy within financial realm for actual problems concerning raising the funds for early retirement plans. It puts forward a portfolio strategy based on bonds and savings. Then, it sets up three mathematical models: the fixed income model, the floating income model and the continuous investment model based on floating income. Furthermore, it goes into detail the basic principle and the calculation steps of the simplex algorithm. In addition, it puts forward a method about finding out a basic feasible solution in order to use the simplex algorithm to solve this kind of models.
All of the mathematical models put forward in the text are linear models. However, the continuous investment model differs from the continuous single period's investment models or the several periods' investment models within stock certificate's portfolio realm. It adopts the method of continuous supplemental investment year by year and deduces new constraints, then solves and analyzes the model. In addition, the article aims at an actual problem concerning raising the funds for early retirement plans, solving each model quantificational, then analyzes through a contrast and gives a reasonable investment suggestion which is useful in actually. However, the continuous investment model has not display advantage in this actually problem, it may surpass the other models and have better applied foreground for large investment plans.
In this article, it doesn't consider the influence of the factors, such as trade tax etc, upon the portfolio strategy. Therefore, it can join trade tax and join various stock certificates, for example, stocks, funds etc, into the portfolio strategy in the future, it can also make use of the different risk norms to draw up a more excellent strategy.
引文
[1]荣喜民,崔红岩.基于偏度的多期组合投资调整模型.天津:天津大学,2005.
[2]马国顺,何广平,王荫清,含风险的多项目投资组合决策分析[A],乌杰,系统科学理论与应用[C],成都:四川大学出版社,1996,635-640.
[3]陈伟忠,孙奉军.组合投资与投资基金管理.北京:中国金融出版社,2004:08-01.
[4]Markowitz H.Portfolio selection[J].Journal of Finance,1952,7,(1):77291.
[5]Carlsson,C.,Fuller,R.,On possibilistic mean value and variance of fuzzy numbers,Fuzzy Sets and Systems,2001,122:351-326.
[6]刘善存,邱菀华.均值-方差模型有效组合投资的一个简单算法.北京航空航天大学学报(社会科学版),2001.
[7]程耿东.工程结构优化设计.水利电力出版社,1983.
[8]俞玉森,数学规划的原理和方法[M],武汉:华中工学院出版社,1985.
[9]《运筹学》教材编写组,运筹学(修订版)[M],北京:清华大学出版社,1997,110.
[10]吴清烈,尤海燕,运筹学[M],南京:东南大学出版社,2004,97.
[11]徐成贤,陈志平,李乃成.近代优化方法.北京:科学出版社,2002.
[12]李红岚,武玉宁.提前退休问题研究.经济理论与经济管理.2002.
[13]程希骏,庄国强,现代投资理论分析[M],合肥:安徽教育出版社,1994.
[14]庄新田,黄小原,卢新,证券组合的模糊优化,东北大学学报(自然科学版),2001,22(2):165-168.
[15]牟太勇,周宗放.多期组合投资权序列矩阵及其应用[J].中国管理科学,2003,(11):1812183.
[16]阿春香.组合投资模型及其算法研究.西安电子科技大学网刊.2005.
[17]何广平.多项目投资决策的一种数学规划模型.宝鸡文理学院学报(自然科学版).2001.
[18]Watada,J.,Fuzzy portolio model for decision making in investment,in:Dynamical Aspects in fuzzy decision making.Physica Verlag,Heidelberg,2001,141-162.
[19]Li D,WL Ng.Optimal dynamic Portfolio selection:multi2period mean2variance formulation[J].Mathematical Finance,2000,10(3)
[20]张忠桢.凸规划—投资组合与网络优化的旋转算法.武汉:武汉大学出版社,2004.
[2]马国顺,何广平,王荫清,含风险的多项目投资组合决策分析[A],乌杰,系统科学理论与应用[C],成都:四川大学出版社,1996,635-640.
[3]陈伟忠,孙奉军.组合投资与投资基金管理.北京:中国金融出版社,2004:08-01.
[4]Markowitz H.Portfolio selection[J].Journal of Finance,1952,7,(1):77291.
[5]Carlsson,C.,Fuller,R.,On possibilistic mean value and variance of fuzzy numbers,Fuzzy Sets and Systems,2001,122:351-326.
[6]刘善存,邱菀华.均值-方差模型有效组合投资的一个简单算法.北京航空航天大学学报(社会科学版),2001.
[7]程耿东.工程结构优化设计.水利电力出版社,1983.
[8]俞玉森,数学规划的原理和方法[M],武汉:华中工学院出版社,1985.
[9]《运筹学》教材编写组,运筹学(修订版)[M],北京:清华大学出版社,1997,110.
[10]吴清烈,尤海燕,运筹学[M],南京:东南大学出版社,2004,97.
[11]徐成贤,陈志平,李乃成.近代优化方法.北京:科学出版社,2002.
[12]李红岚,武玉宁.提前退休问题研究.经济理论与经济管理.2002.
[13]程希骏,庄国强,现代投资理论分析[M],合肥:安徽教育出版社,1994.
[14]庄新田,黄小原,卢新,证券组合的模糊优化,东北大学学报(自然科学版),2001,22(2):165-168.
[15]牟太勇,周宗放.多期组合投资权序列矩阵及其应用[J].中国管理科学,2003,(11):1812183.
[16]阿春香.组合投资模型及其算法研究.西安电子科技大学网刊.2005.
[17]何广平.多项目投资决策的一种数学规划模型.宝鸡文理学院学报(自然科学版).2001.
[18]Watada,J.,Fuzzy portolio model for decision making in investment,in:Dynamical Aspects in fuzzy decision making.Physica Verlag,Heidelberg,2001,141-162.
[19]Li D,WL Ng.Optimal dynamic Portfolio selection:multi2period mean2variance formulation[J].Mathematical Finance,2000,10(3)
[20]张忠桢.凸规划—投资组合与网络优化的旋转算法.武汉:武汉大学出版社,2004.