英文标题：
《Portfolio Optimization with Entropic Value-at-Risk》
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作者：
Amir Ahmadi-Javid and Malihe Fallah-Tafti
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最新提交年份：
2017
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英文摘要：
  The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, while well-known monotone risk measures, such as VaR and CVaR lack these properties. A key feature for a risk measure, besides its financial properties, is its applicability in large-scale sample-based portfolio optimization. If the negative return of an investment portfolio is a differentiable convex function, the portfolio optimization with the EVaR results in a differentiable convex program whose number of variables and constraints is independent of the sample size, which is not the case for the VaR and CVaR. This enables us to design an efficient algorithm using differentiable convex optimization. Our extensive numerical study shows the high efficiency of the algorithm in large scales, compared to the existing convex optimization software packages. The computational efficiency of the EVaR portfolio optimization approach is also compared with that of CVaR-based portfolio optimization. This comparison shows that the EVaR approach generally performs similarly, and it outperforms as the sample size increases. Moreover, the comparison of the portfolios obtained for a real case by the EVaR and CVaR approaches shows that the EVaR approach can find portfolios with better expectations and VaR values at high confidence levels.
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中文摘要：
熵风险值（EVaR）是一种新的一致性风险度量，它是风险值（VaR）和条件风险值（CVaR）的上界。作为重要的性质，EVaR在其域上是强单调的，在包括所有连续分布的广泛子域上是严格单调的，而著名的单调风险度量，如VaR和CVaR缺乏这些性质。除了金融属性外，风险度量的一个关键特征是其在大规模基于样本的投资组合优化中的适用性。如果投资组合的负收益是一个可微凸函数，那么使用EVaR的投资组合优化会产生一个可微凸规划，其变量和约束的数量与样本量无关，而VaR和CVaR则不是这种情况。这使我们能够使用可微凸优化设计一个有效的算法。我们广泛的数值研究表明，与现有的凸优化软件包相比，该算法在大范围内具有较高的效率。还比较了EVaR投资组合优化方法与基于CVaR的投资组合优化方法的计算效率。这一比较表明，EVaR方法通常表现类似，并且随着样本量的增加，其表现会更好。此外，对EVaR和CVaR方法在实际案例中获得的投资组合进行比较表明，EVaR方法可以在高置信水平下找到具有更好期望和VaR值的投资组合。
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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：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：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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