英文标题：
《Dynamic Mean-LPM and Mean-CVaR Portfolio Optimization in Continuous-time》
---
作者：
Jianjun Gao, Ke Zhou, Duan Li and Xiren Cao
---
最新提交年份：
2014
---
英文摘要：
Instead of controlling \"symmetric\" risks measured by central moments of investment return or terminal wealth, more and more portfolio models have shifted their focus to manage \"asymmetric\" downside risks that the investment return is below certain threshold. Among the existing downside risk measures, the lower-partial moments (LPM) and conditional value-at-risk (CVaR) are probably most promising. In this paper we investigate the dynamic mean-LPM and mean-CVaR portfolio optimization problems in continuous-time, while the current literature has only witnessed their static versions. Our contributions are two-fold, in both building up tractable formulations and deriving corresponding analytical solutions. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the class of mean-downside risk portfolio models. The limit funding level not only enables us to solve both dynamic mean-LPM and mean-CVaR portfolio optimization problems, but also offers a flexibility to tame the aggressiveness of the portfolio policies generated from such mean - downside risk models. More specifically, for a general market setting, we prove the existence and uniqueness of the Lagrangian multiplies, which is a key step in applying the martingale approach, and establish a theoretical foundation for developing efficient numerical solution approaches. Moreover, for situations where the opportunity set of the market setting is deterministic, we derive analytical portfolio policies for both dynamic mean-LPM and mean-CVaR formulations.
---
中文摘要：
越来越多的投资组合模型不再控制以投资回报或终端财富的中心时刻衡量的“对称”风险，而是将重点转移到管理投资回报低于一定阈值的“不对称”下行风险上。在现有的下行风险度量中，较低偏矩（LPM）和条件风险价值（CVaR）可能是最有前途的。在本文中，我们研究了连续时间内的动态平均LPM和平均CVaR投资组合优化问题，而目前的文献只看到了它们的静态版本。我们的贡献有两方面，一方面是建立易于处理的公式，另一方面是推导相应的分析解。通过对终端财富施加有限的融资水平，我们克服了平均下行风险投资组合模型中表现出的不适性。极限融资水平不仅使我们能够解决动态平均LPM和平均CVaR投资组合优化问题，而且还提供了一种灵活性，以抑制这种平均下行风险模型产生的投资组合政策的攻击性。更具体地说，对于一般的市场环境，我们证明了拉格朗日乘数的存在性和唯一性，这是应用鞅方法的关键步骤，并为发展有效的数值解方法奠定了理论基矗此外，对于市场环境的机会集具有确定性的情况，我们推导了动态平均LPM和平均CVaR公式的分析性投资组合政策。
---
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
--

---
PDF下载：
-->