7 papers
Affine Structure of the Brownian Signature
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We establish an infinite-dimensional affine transform theory for the time-augmented Brownian signature. Our first main result shows that, for a suitable class of linear functions o…
Stochastic control with signatures via Riccati equations on the tensor algebra
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We solve in semi-explicit form a class of non-Markovian stochastic optimal control problems with path-dependent rewards, using path signatures. We reformulate the control problem a…
Volterra clocks and their pure-jump limits: hitting times of curved boundaries
Eduardo Abi Jaber, Elie Attal, Andreas Sojmark
We introduce a class of continuous Volterra processes, called Volterra clocks, and study their singular limit as the memory kernel collapses to a Dirac mass at zero. The dynamics a…
Efficient Simulation of Hawkes Processes using their Affine Volterra Structure
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the in…
Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussian
Eduardo Abi Jaber, Elie Attal
We introduce a novel simulation scheme, iVi (integrated Volterra implicit), for integrated Volterra square-root processes and Volterra Heston models based on the Inverse Gaussian d…
From Hyper Roughness to Jumps as
Eduardo Abi Jaber, Elie Attal, Mathieu Rosenbaum
We investigate the weak limit of the hyper-rough square-root process as the Hurst index goes to . This limit corresponds to the fractional kernel losing…