A general theorem shows that neural networks inherit the absence of the curse of dimensionality from any discrete Monte Carlo scheme they can emulate, with applications to Kolmogorov PDEs.
Deep Curve-dependent PDEs for affine rough volatility
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abstract
We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE (CPDE), depending on forward curves rather than the whole path of the process, for which we develop a numerical scheme based on deep learning techniques. Numerical simulations suggest that the latter is a promising alternative to classical Monte Carlo simulations.
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Deep neural network approximations for Monte Carlo algorithms
A general theorem shows that neural networks inherit the absence of the curse of dimensionality from any discrete Monte Carlo scheme they can emulate, with applications to Kolmogorov PDEs.