英文标题：
《Optimal Derivative Liquidation Timing Under Path-Dependent Risk
Penalties》
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作者：
Tim Leung and Yoshihiro Shirai
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最新提交年份：
2015
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英文摘要：
This paper studies the risk-adjusted optimal timing to liquidate an option at the prevailing market price. In addition to maximizing the expected discounted return from option sale, we incorporate a path-dependent risk penalty based on shortfall or quadratic variation of the option price up to the liquidation time. We establish the conditions under which it is optimal to immediately liquidate or hold the option position through expiration. Furthermore, we study the variational inequality associated with the optimal stopping problem, and prove the existence and uniqueness of a strong solution. A series of analytical and numerical results are provided to illustrate the non-trivial optimal liquidation strategies under geometric Brownian motion (GBM) and exponential Ornstein-Uhlenbeck models. We examine the combined effects of price dynamics and risk penalty on the sell and delay regions for various options. In addition, we obtain an explicit closed-form solution for the liquidation of a stock with quadratic penalty under the GBM model.
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中文摘要：
本文研究了在当前市场价格下，风险调整后的最优期权变现时机。除了最大化期权销售的预期贴现回报外，我们还加入了基于期权价格短缺或二次变化直至清算时间的路径依赖风险惩罚。我们确定了立即清算或持有期权头寸直至到期的最佳条件。此外，我们还研究了与最优停止问题相关的变分不等式，并证明了强解的存在唯一性。本文给出了一系列分析和数值结果，以说明几何布朗运动（GBM）和指数Ornstein-Uhlenbeck模型下的非平凡最优清算策略。我们研究了价格动态和风险惩罚对各种期权的卖出和延迟区域的综合影响。此外，我们还得到了GBM模型下具有二次惩罚的股票清算的显式闭式解。
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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
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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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