Fast Sampling from Time-Integrated Bridges using Deep Learning

TL;DR

This paper introduces a fast, neural network-based method for sampling from conditioned time-integrated stochastic bridges, achieving high accuracy and efficiency, with applications demonstrated in finance.

Contribution

It presents a novel data-driven approach combining polynomial chaos and neural networks to efficiently sample from conditioned time-integrated stochastic processes.

Findings

High-accuracy sampling in milliseconds

Robust neural network approximation of collocation points

Effective application to financial models

Abstract

We propose a methodology to sample from time-integrated stochastic bridges, namely random variables defined as $\int_{t_1}^{t_2} f(Y(t))dt$ conditioned on $Y(t_1)\!=\!a$ and $Y(t_2)\!=\!b$, with $a,b\in R$. The Stochastic Collocation Monte Carlo sampler and the Seven-League scheme are applied for this purpose. Notably, the distribution of the time-integrated bridge is approximated utilizing a polynomial chaos expansion built on a suitable set of stochastic collocation points. Furthermore, artificial neural networks are employed to learn the collocation points. The result is a robust, data-driven procedure for the Monte Carlo sampling from conditional time-integrated processes, which guarantees high accuracy and generates thousands of samples in milliseconds. Applications, with a focus on finance, are presented here as well.