论文标题
深度二次对冲
Deep Quadratic Hedging
论文作者
论文摘要
我们提出了一种新的计算程序，用于在高维不完整的市场中进行二次对冲，涵盖均值变化对冲和局部风险最小化。从从向后的随机微分方程（BSDE）的角度来看，可以对两种二次方法进行观察，我们（递归地）采用了深度学习的BSDE求解器来计算整个最佳套期策略路径。这使我们能够克服维度的诅咒，从而扩大了高维度中二次对冲的适用范围。我们使用经典的赫斯顿模型和多重速率概括测试我们的方法，这表明这导致了高度的准确性。
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.
