We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer’s pathwise Itô calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space. Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.

中文翻译：

---

一类Delta套期保值策略中的无路径套利

我们考虑基于Föllmer的路径式Itô微积分对Delta套期保值异国期权进行严格的路径设置。价格轨迹是d维连续函数，其沿路径的二次方变化和协方差由给定的局部波动率矩阵确定。通过对抛物型柯西问题的递归方案的存在结果以及在路径空间上存在功能性柯西问题的存在，建立了这种对冲策略中Delta套期保值策略的存在。我们的主要结果建立了在包含这些Delta套期保值策略的策略类别中以及在相对温和的条件下本地波动率矩阵中不存在循序套利机会的情况。