英文标题：
《Portfolio Optimization under Shortfall Risk Constraint》
---
作者：
Oliver Janke and Qinghua Li
---
最新提交年份：
2016
---
英文摘要：
  This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility function and the loss function, we find an optimal wealth process for the constrained problem and characterize the bi-dual relation between the respective value functions of the constrained problem and its dual. This approach applies to both complete and incomplete markets. Moreover, the extension to more complicated cases is illustrated by solving the problem with a consumption process added. Finally, we give an example of utility and loss functions in the Black-Scholes market where the solutions have explicit forms.
---
中文摘要：
本文提出了一种利用拉格朗日乘子和凸对偶的方法来解决基于效用的短缺风险约束下的效用最大化问题。在效用函数和损失函数渐近弹性的温和条件下，我们找到了约束问题的最优财富过程，并刻画了约束问题各自的值函数与其对偶之间的双对偶关系。这种方法适用于完全市场和不完全市场。此外，通过添加消耗过程来解决问题，说明了对更复杂情况的扩展。最后，我们给出了Black-Scholes市场中效用函数和损失函数的一个例子，其中解具有显式形式。
---
分类信息：

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
--
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：
-->