标题： 尾部安全的随机控制SPX-VIX对冲：人工智能敏感性与无套利市场动态之间的白盒桥梁 显示英文标题

标题： Tail-Safe Stochastic-Control SPX-VIX Hedging: A White-Box Bridge Between AI Sensitivities and Arbitrage-Free Market Dynamics

摘要： 我们提出了一种白盒、风险敏感的框架，在交易成本和制度变化下共同对冲标普500指数（SPX）和波动率指数（VIX）头寸。该方法将无套利市场教师与一个通过约束强制安全的控制层相结合。在市场方面，我们整合了一个基于SSVI的隐含波动率曲面和一个符合Cboe规则的VIX计算（包括翼部修剪和30天插值），并通过一个截断的、保持凸性的Dupire局部波动率提取器将价格与动态连接起来。在控制方面，我们将对冲问题建模为一个小的二次规划问题，其中包含用于库存、利率和尾部风险的控制障碍函数（CBF）框；一个充分下降的执行门控，仅在风险下降足以证明成本时进行交易；以及三个针对性的尾部安全升级：相关性/期限感知的VIX权重、受保护的不交易带和期限感知的微交易阈值及冷却期。我们证明了每一步QP的存在性/唯一性以及KKT正则性，安全集的前向不变性，当门控打开时的一步风险下降，以及在有界交易速率下的无振荡性。对于动态层，我们建立了离散Dupire估计量的正性和二阶一致性，并给出了一个索引一致性边界，将教师VIX与具有显式求积和投影误差的CIR风格代理联系起来。在一个可重复的合成环境中，该控制器在减少预期不足的同时抑制了不必要的换手率，而教师-曲面构建保持了指数级残差的小且稳定。 显示英文摘要

摘要： We present a white-box, risk-sensitive framework for jointly hedging SPX and VIX exposures under transaction costs and regime shifts. The approach couples an arbitrage-free market teacher with a control layer that enforces safety as constraints. On the market side, we integrate an SSVI-based implied-volatility surface and a Cboe-compliant VIX computation (including wing pruning and 30-day interpolation), and connect prices to dynamics via a clipped, convexity-preserving Dupire local-volatility extractor. On the control side, we pose hedging as a small quadratic program with control-barrier-function (CBF) boxes for inventory, rate, and tail risk; a sufficient-descent execution gate that trades only when risk drop justifies cost; and three targeted tail-safety upgrades: a correlation/expiry-aware VIX weight, guarded no-trade bands, and expiry-aware micro-trade thresholds with cooldown. We prove existence/uniqueness and KKT regularity of the per-step QP, forward invariance of safety sets, one-step risk descent when the gate opens, and no chattering with bounded trade rates. For the dynamics layer, we establish positivity and second-order consistency of the discrete Dupire estimator and give an index-coherence bound linking the teacher VIX to a CIR-style proxy with explicit quadrature and projection errors. In a reproducible synthetic environment mirroring exchange rules and execution frictions, the controller reduces expected shortfall while suppressing nuisance turnover, and the teacher-surface construction keeps index-level residuals small and stable.