极端依赖下的压力法则模拟：生成模型必须保留的特征
Simulating Stress Laws under Extremal Dependence: Characterizing What Generative Models Must Preserve
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中文总结 AI 辅助
该研究针对多元重尾风险因子驱动的系统，提出SSGEN方法以保留极端依赖下的压力法则，解决稀有压力场景生成问题并建立收敛速率。
中文摘要 AI 辅助
我们研究由多元重尾风险因子驱动的系统的压力场景生成。在多个金融损失同时处于极端值的区域内，压力分析既关注风险因子的条件法则，也关注产生这些损失的最可能构型。我们证明两者受同一极限尾法则支配。保留其测度可恢复稀有事件概率与缩放后的条件压力法则，而对极端依赖的错误设定会扭曲部分常规联合压力概率。该法则的密度支配反向压力优化，其最大化器可识别最可能的压力构型。为在有限样本中利用这一共同结构，我们开发SSGEN（自相似生成估计），它从中间超限中学习极端依赖，并利用帕累托径向分量外推至更稀有水平。即使样本中不存在目标事件，我们也为生成的条件法则及数据驱动的反向压力解建立了收敛速率。
英文摘要
We study stress-scenario generation for systems driven by multivariate heavy-tailed risk factors. Within regions where several financial losses are simultaneously extreme, stress analysis concerns both the conditional law of the risk factors and the most plausible configurations producing those losses. We show that both are governed by the same limiting tail law. Preserving its measure recovers rare-event probabilities and scaled conditional stress laws, while misspecifying extremal dependence distorts some regular joint-stress probability. Its density governs reverse-stress optimization, whose maximizers identify the most plausible stress configurations. To exploit this common structure in finite samples, we develop SSGEN (Self-Similar Generative Estimation), which learns extremal dependence from intermediate exceedances and extrapolates to rarer levels using a Pareto radial component. Even when the target event is absent from the sample, we establish convergence rates for the generated conditional law, and data-driven reverse-stress solutions.
