1 code implementation • 27 Oct 2022 • Nicolas Privault, Michèle Thieullen
We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition.
no code implementations • 28 Sep 2022 • Jiang Yu Nguwi, Nicolas Privault
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using regression.
1 code implementation • 7 Mar 2022 • Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault
We present a multidimensional deep learning implementation of a stochastic branching algorithm for the numerical solution of fully nonlinear PDEs.
no code implementations • 9 Dec 2021 • Zhe Wang, Nicolas Privault, Claude Guet
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks, respectively.
1 code implementation • 25 Oct 2021 • Nicolas Privault
The purpose of this paper is to present a recursive algorithm and its implementation in Maple and Mathematica for the computation of joint moments and cumulants of Hawkes processes with exponential kernels.
no code implementations • 20 Apr 2021 • Jean-Christophe Breton, Youssef El-Khatib, Jun Fan, Nicolas Privault
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates.
