英文标题：
《Macroscopic theorem of the portfolio optimization problem with a
  risk-free asset》
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作者：
Ippei Suzuki and Takashi Shinzato
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最新提交年份：
2019
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英文摘要：
  The investment risk minimization problem with budget and return constraints has been the subject of research using replica analysis but there are shortcomings in the extant literature. With respect to Tobin\'s separation theorem and the capital asset pricing model, it is necessary to investigate the implications of a risk-free asset and examine its influence on the optimal portfolio. Accordingly, in this work, we explore the investment risk minimization problem in the presence of a risk-free asset with budget and return constraints. Moreover, we discuss opportunity loss, the Pythagorean theorem of the Sharpe ratio, and Tobin\'s separation theorem.
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中文摘要：
预算和回报约束下的投资风险最小化问题一直是副本分析研究的主题，但现有文献中存在不足。关于托宾分离定理和资本资产定价模型，有必要研究无风险资产的含义，并检查其对最优投资组合的影响。因此，在这项工作中，我们探讨了存在预算和回报约束的无风险资产的投资风险最小化问题。此外，我们还讨论了机会损失、毕达哥拉斯夏普比定理和托宾分离定理。
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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：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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