超越布朗运动的回撤风险：蒙特卡洛框架、非高斯扩展与长记忆
Drawdown Risk Beyond Brownian Motion: A Monte-Carlo Framework, Non-Gaussian Extensions, and Long Memory
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中文总结 AI 辅助
该研究基于Rej等人的回撤框架，通过蒙特卡洛实验、非高斯扩展和长记忆替换，揭示回撤风险的影响因素，提供可复现查找表与校准方法。
中文摘要 AI 辅助
给定一个系统化交易策略的夏普比率及其收益的统计结构，该策略的回撤应达到多深、持续多久？我们基于Rej、Seager和Bouchaud（2017）的回撤框架，分三步给出答案：首先，将他们的闭式结果重新表述为透明的蒙特卡洛实验，对照其分析基准进行验证，并扩展回撤到四个与决策相关的指标的映射：最大回撤、最大损失、最终负时间和最长恢复时间；随后，在保持真实夏普比率和波动率固定的前提下，放松高斯假设，在不同策略原型中改变偏度、厚尾、波动率聚类和夏普估计不确定性，发现四个指标的变化存在差异，单一的高斯表格会给出错误预警；最后，将短记忆持续性替换为分数布朗运动，表明在持续性下回撤风险的表观放大，对于最大回撤深度而言，几乎完全是自相似分散缩放（T^(H-1/2)）而非路径几何，这是平方根时间校准的失效，而非内在危险。我们提供可复现的查找表和实用校准方法。
英文摘要
How deep and how long should the drawdowns of a systematic trading strategy run, given its Sharpe ratio and the statistical structure of its returns? Building on the drawdown framework of Rej, Seager and Bouchaud (2017), we develop the answer in three steps. We first reframe their closed-form results as a transparent Monte-Carlo experiment, validate it against their analytic benchmarks, and extend the mapping from drawdowns to four decision-relevant measures: maximum drawdown, maximum loss, final negative time and longest recovery time. We then relax the Gaussian assumption, holding the true Sharpe and volatility fixed while varying skewness, fat tails, volatility clustering and Sharpe-estimation uncertainty across strategy archetypes; the four measures move differently, so a single Gaussian table mis-warns. We finally replace short-memory persistence with fractional Brownian motion and show that the apparent amplification of drawdown risk under persistence is, for maximum-drawdown depth, almost entirely self-similar dispersion scaling (T^(H-1/2)) rather than path geometry: a failure of square-root-of-time calibration, not intrinsic danger. We provide reproducible lookup tables and a practical calibration recipe.
