标题： 在路径依赖风险惩罚下的最优衍生品清算时机 显示英文标题

标题： Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties

摘要： 本文研究在当前市场价格下卖出期权的风险调整最优时机。 除了最大化期权出售的预期贴现收益外，我们还引入了一个基于卖出前期权价格不足或二次变差的路径依赖风险惩罚项。 我们建立了在何时立即卖出或持有期权直至到期最优的条件。 此外，我们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性和唯一性。 提供了一系列分析和数值结果，以说明在几何布朗运动（GBM）和指数奥恩斯坦-乌伦贝克模型下的非平凡最优卖出策略。 我们考察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，我们在GBM模型下获得了具有二次惩罚的股票卖出的显式闭合解。 显示英文摘要

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.