Fast sampling from time-integrated bridges using deep learning

We propose a methodology for sampling from time-integrated stochastic bridges, i.e., random variables defined as ∫t1t2f(Y(t))dt conditional on Y(t1)=a and Y(t2)=b, with a,b∈R. The techniques developed in Grzelak et al. (2019) – the Stochastic Collocation Monte Carlo sampler Liu (2020) Seven-League scheme are applied this purpose. Notably, bridge distribution is approximated using polynomial chaos expansion constructed over an appropriate set of collocation points. In addition, artificial neural networks employed to learn result robust, data-driven procedure processes, which guarantees high accuracy generates thousands samples milliseconds. Applications also presented, focus finance.