We propose a novel computational procedure for quadratic hedging in high-dimensional incomplete markets, covering mean-variance hedging and local risk minimization. Starting from the observation that both quadratic approaches can be treated from the point of view of backward stochastic differential equations (BSDEs), we (recursively) apply a deep learning-based BSDE solver to compute the entire optimal hedging strategies paths. This allows us to overcome the curse of dimensionality, extending the scope of applicability of quadratic hedging in high dimension. We test our approach with a classic Heston model and with a multiasset and multifactor generalization thereof, showing that this leads to high levels of accuracy.

翻译：本文提出了一种用于高维不完全市场中二次对冲的新型计算流程，涵盖均值-方差对冲与局部风险最小化方法。基于两种二次方法均可从倒向随机微分方程视角处理的观察，我们（递归地）应用基于深度学习的BSDE求解器来计算完整的最优对冲策略路径。该方法使我们能够克服维度灾难，从而拓展二次对冲在高维场景中的适用范围。我们通过经典Heston模型及其多资产多因子推广模型进行测试，结果表明该方法具有很高的计算精度。