【作者】 李慧丹；

【导师】 冯恩民；

【作者基本信息】 大连理工大学 ， 金融数学与保险精算， 2008， 硕士

【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。更多还原

【Abstract】 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.更多还原