TY - UNPB
T1 - Fast Sampling from Time-Integrated Bridges using Deep Learning
AU - Perotti, Leonardo
AU - Grzelak, Lech A.
PY - 2021/11/27
Y1 - 2021/11/27
N2 - 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.
AB - 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.
KW - q-fin.CP
U2 - 10.48550/arXiv.2111.13901
DO - 10.48550/arXiv.2111.13901
M3 - Preprint
BT - Fast Sampling from Time-Integrated Bridges using Deep Learning
PB - arXiv
ER -