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Solving Portfolio Optimization Problem Based on Extension Principle

机译：基于扩展原理解决产品组合优化问题

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Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately predicted by historical data. However, no matter how accurate the past data is, this premise will not exist in the financial market due to the high volatility of market environment. This paper discusses the fuzzy portfolio optimization problem where the asset returns are represented by fuzzy data. A mean-absolute deviation risk function model and Zadeh's extension principle are utilized for the solution method of portfolio optimization problem with fuzzy returns. Since the parameters are fuzzy numbers, the gain of return is a fuzzy number as well, A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the return of the portfolio optimization problem. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a pair of ordinary one-level linear programs so they can be manipulated. It is found that the calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on, the greater the potential return. An example illustrates the whole idea on fuzzy portfolio optimization problem.
机译：传统的投资组合优化模型假设可以通过历史数据准确预测股票市场的未来状况。然而，无论过去数据如何准确，由于市场环境的高波动性，金融市场中的前提将不存在。本文讨论了模糊组合优化问题，其中资产返回由模糊数据表示。平均绝对偏差风险函数模型和Zadeh的扩展原理用于模糊回报的组合优化问题解决方法。由于参数是模糊数，因此返回的增益也是模糊数，因此配制了一对两级数学程序，以计算投资组合优化问题的返回的上限和下限。基于二元定理和通过应用可变变换技术，将一对两级数学程序转换为一对普通的单级线性程序，以便操纵它们。结果发现，计算结果符合财经和经济学的重要思想，即投资者愿意承担的风险越大，潜在回报越大。一个例子说明了模糊组合优化问题的整个想法。

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