Neural variance reduction for stochastic differential equations

Abstract

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.

arXiv commentUpdated version

References in corpus (6)

• Adam: A Method for Stochastic Optimization
• DGM: A deep learning algorithm for solving partial differential equations
• The Modern Mathematics of Deep Learning
• Uniform error estimates for artificial neural network approximations for heat equations
• Variance reduction for discretised diffusions via regression
• Unbiased deep solvers for linear parametric PDEs

Cited by in corpus (2)

• Double-Loop Importance Sampling for McKean--Vlasov Stochastic Differential Equation
• Deep learning of transition probability densities for stochastic asset models with applications in option pricing