Fast Sampling from Time-Integrated Bridges using Deep Learning

Leonardo Perotti and Lech Grzelak

Papers from arXiv.org

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.

Date: 2021-11
New Economics Papers: this item is included in nep-big and nep-cmp
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