论文标题
随机微分方程的神经差异降低
Neural variance reduction for stochastic differential equations
论文作者
论文摘要
降低方差技术对于蒙特卡洛模拟在金融应用中的效率至关重要。我们建议使用神经SDE的使用，具有由神经网络参数参数的控制变量，以学习近似最佳的控制变体，因此随着SDE的轨迹的模拟，降低了方差。我们认为由布朗运动驱动的SDE，更普遍地是由包括无限活性的莱维工艺所驱动的。对于后一种情况，我们证明了降低方差的最佳条件。提出了选项定价的几个数值示例。
Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn approximately optimal control variates and hence reduce variance as trajectories of the SDEs are being simulated. We consider SDEs driven by Brownian motion and, more generally, by Lévy processes including those with infinite activity. For the latter case, we prove optimality conditions for the variance reduction. Several numerical examples from option pricing are presented.
