路径依赖风险惩罚下的最优衍生品清算时机
Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties
摘要：
本文研究了在当前市场价格下风险调整后的期权最优变现时机问题。除了最大化期权销售的预期贴现收益外，我们还引入了基于期权价格到清算时间的短缺或二次变化的路径依赖风险惩罚。我们建立的条件下，它是最佳的立即清算或持有期权的立场，直到到期。进一步研究了与最优停时问题相关的变分不等式，证明了强解的存在唯一性。给出了几何布朗运动（GBM）和指数Ornstein-Uhlenbeck模型下的非平凡最优清算策略的一系列解析和数值结果.我们研究了各种期权的价格动态和风险惩罚对卖出和延迟区域的综合影响。此外，我们得到了一个显式的封闭形式的解决方案，在GBM模型下的二次罚款的股票清算。
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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