英文标题：
《Spin Glasses and Nonlinear Constraints in Portfolio Optimization》
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作者：
M. Andrecut
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最新提交年份：
2013
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英文摘要：
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.
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中文摘要：
讨论了强制存款约束下的投资组合优化问题。最近的研究表明，由于这种非线性约束，解决方案由大量指数级的最优投资组合组成，彼此完全不同，对问题输入参数的任何变化都极为敏感，这使得理性决策的概念受到质疑。在这里，我们使用二次约束来重新描述这个问题，并且我们表明，从物理学的角度来看，找到一个最优投资组合相当于计算一个具有恒定磁化范数约束的随机伊辛模型的平均场磁化。我们证明了该模型简化为一个特征问题，有2N个解，其中N是定义投资组合的资产数量。此外，为了说明我们的结果，我们给出了一个在纳斯达克市场上交易的几个高风险普通股的投资组合的详细数字示例。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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