英文标题：
《On Dynamic Deviation Measures and Continuous-Time Portfolio Optimisation》
---
作者：
Martijn Pistorius and Mitja Stadje
---
最新提交年份：
2016
---
英文摘要：
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of backward SDEs. We establish for any dynamic deviation measure an integral representation, and derive a dual characterisation result in terms of additively $m$-stable dual sets. Using this notion of dynamic deviation measure we formulate a dynamic mean-deviation portfolio optimisation problem in a jump-diffusion setting and identify a subgame-perfect Nash equilibrium strategy that is linear as function of wealth by deriving and solving an associated extended HJB equation.
---
中文摘要：
在本文中，我们提出了动态偏差度量的概念，作为偏差度量（静态）概念的动态时间一致性扩展。为了实现时间一致性，我们要求动态偏差度量满足广义条件方差公式。我们证明了在控制条件下，动态偏差测度被刻画为一类向后SDE的解。我们为任何动态偏差度量建立了一个积分表示，并导出了一个关于附加$m$-稳定对偶集的对偶特征化结果。利用动态偏差测度的概念，我们在跳跃-扩散环境下建立了一个动态均值-偏差投资组合优化问题，并通过推导和求解相关的扩展HJB方程，确定了一个与财富成线性函数的子博弈完美纳什均衡策略。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
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
--
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
--

---
PDF下载：
-->