Portfolio Selection Models with Technical Analysis-Based Fuzzy Birandom Variables
Portfolio Selection Models with Technical Analysis-Based Fuzzy Birandom Variables
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DOI：
10.1587/transinf.e97.d.11
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
You Li;Bo Wang;J. Watada
中科院分区：
文献类型：
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作者：
You Li;Bo Wang;J. Watada
最近，模糊集理论已被广泛用于建立投资组合模型中的不确定性发挥作用。在这些模型中，一般将未来的证券收益率作为模糊变量，然后建立数学模型，根据给定的风险水平使投资收益最大化，或在固定收益水平的基础上使风险水平最小化。本文在已有工作的基础上，提出了一种基于模糊双随机变量的投资组合选择模型。本研究的创新之处在于：第一，将技术分析的概念与模糊集合理论相结合，将证券收益率作为模糊双随机变量。其次，利用模糊双随机风险价值（VaR）建立了基于模糊双随机风险价值的投资组合选择模型（FBVaR-PSM）。VaR模型能够直接反映在给定置信水平下所选案例的最大损失，比其他模型更敏感，比传统的风险度量方法更容易为一般投资者所接受。为了求解FBVaR-PSM，在证券收益率为梯形、三角形或高斯型模糊双随机变量的特殊情况下，推导了FBVaR-PSM的几种清晰等价模型，这些模型可以用任何线性规划求解器来处理。一般而言，模糊双随机模拟粒子群优化算法（FBS-PSO）的目的是找到近似的最优解。为了说明所提出的模型和FBS-PSO的行为，两个数值例子介绍了基于投资者的不同风险态度。最后，我们分析了实验结果，并提供了一些现有的方法进行讨论。关键词：投资组合选择，技术分析，模糊双随机变量，风险价值，模糊双随机模拟，粒子群优化
Recently, fuzzy set theory has been widely employed in building portfolio selection models where uncertainty plays a role. In these models, future security returns are generally taken for fuzzy variables and mathematical models are then built to maximize the investment profit according to a given risk level or to minimize a risk level based on a fixed profit level. Based on existing works, this paper proposes a portfolio selection model based on fuzzy birandom variables. Two original contributions are provided by the study: First, the concept of technical analysis is combined with fuzzy set theory to use the security returns as fuzzy birandom variables. Second, the fuzzy birandom Value-at-Risk (VaR) is used to build our model, which is called the fuzzy birandom VaR-based portfolio selection model (FBVaR-PSM). The VaR can directly reflect the largest loss of a selected case at a given confidence level and it is more sensitive than other models and more acceptable for general investors than conventional risk measurements. To solve the FBVaR-PSM, in some special cases when the security returns are taken for trapezoidal, triangular or Gaussian fuzzy birandom variables, several crisp equivalent models of the FBVaR-PSM are derived, which can be handled by any linear programming solver. In general, the fuzzy birandom simulation-based particle swarm optimization algorithm (FBS-PSO) is designed to find the approximate optimal solution. To illustrate the proposed model and the behavior of the FBS-PSO, two numerical examples are introduced based on investors’ different risk attitudes. Finally, we analyze the experimental results and provide a discussion of some existing approaches. key words: portfolio selection, technical analysis, fuzzy birandom variable, Value-at-Risk, fuzzy birandom simulation, particle swarm optimization