Low-dimensional approximations of the conditional law of Volterra processes: a non-positive curvature approach

Understand

Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance.

• While deep neural network models offer promise in approximating the conditional law of such processes, their effectiveness is hindered by the curse of dimensionality caused by the infinite dimensionality and non-smooth nature of these problems.
• To address this, we propose a two-step solution.
• Firstly, we develop a stable dimension reduction technique, projecting the law of a reasonably broad class of Volterra process onto a low-dimensional statistical manifold of non-positive sectional curvature.