英文标题：
《Replica Analysis for the Duality of the Portfolio Optimization Problem》
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作者：
Takashi Shinzato
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最新提交年份：
2016
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英文摘要：
  In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics, and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
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中文摘要：
本文利用复制分析方法讨论了均值方差模型中由投资风险最小化问题和期望收益最大化问题组成的原对偶问题。作为我们在先前研究中分析的仅在预算约束下的投资风险最小化问题的自然扩展，我们在此考虑一个原始对偶问题，其中具有预算和预期收益约束的投资风险最小化问题被视为原始问题，将具有预算和投资风险约束的期望收益最大化问题视为对偶问题。对于这些优化问题，我们使用统计机械信息学中发展的方法分析了一个涉及这两个优化问题的淬火无序系统，并确认两个最优投资组合都可以具有原始-对偶结构。最后，数值仿真结果验证了该方法的有效性。
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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：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：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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