摘要翻译：
本文研究了在风险值、预期缺口和半方差等下行风险测度下，通过拟合有限样本资产收益的参数分布来估计投资组合优化的可行性和噪声敏感性。我们发现，在这三种情况下，最优解的存在性是一个概率问题，取决于特定的随机样本。在这些问题参数的临界组合中，我们发现一个算法相变，将优化可行的阶段与不可行的阶段分开。这种转变类似于以前发现的基于历史时间序列的预期缺口的转变。我们用复制法计算相图，并求出在临界点发散的估计误差的临界指数。蒙特卡罗模拟验证了分析结果。
---
英文标题：
《The instability of downside risk measures》
---
作者：
Istvan Varga-Haszonits, Imre Kondor
---
最新提交年份：
2008
---
分类信息：

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
--
一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
--

---
英文摘要：
  We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample of asset returns. We find that the existence of the optimum is a probabilistic issue, depending on the particular random sample, in all three cases. At a critical combination of the parameters of these problems we find an algorithmic phase transition, separating the phase where the optimization is feasible from the one where it is not. This transition is similar to the one discovered earlier for Expected Shortfall based on historical time series. We employ the replica method to compute the phase diagram, as well as to obtain the critical exponent of the estimation error that diverges at the critical point. The analytical results are corroborated by Monte Carlo simulations.
---
PDF链接：
https://arxiv.org/pdf/0811.0800