英文标题：
《Pairs Trading under Drift Uncertainty and Risk Penalization》
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作者：
S\\\"uhan Altay, Katia Colaneri and Zehra Eksi
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最新提交年份：
2018
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英文摘要：
In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics. The relationship between pairs, called a spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time, finite-state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to the one with full information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under full and partial information and show that the certainty equivalence principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a toy example with a two-state Markov chain.
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中文摘要：
在这项工作中，我们研究了一个与配对交易相关的动态投资组合优化问题，这是一种将一种证券的多头头寸与另一种具有类似特征的证券的空头头寸相匹配的投资策略。成对之间的关系称为扩散，由高斯均值回复过程建模，其漂移率由不可观测的连续时间有限状态马尔可夫链调制。利用经典的随机过滤理论，我们将部分信息的问题简化为完全信息的问题，并用对数效用函数来解决，其中终端财富根据财富过程的已实现波动率由投资组合的风险来惩罚。我们刻画了完全和部分信息下的最优美元中性策略以及最优价值函数，并证明确定性等价原则适用于最优投资组合策略。最后，我们提供了一个带有两状态马尔可夫链的玩具实例的数值分析。
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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：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
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