12 citations · 19 across the 29 of their papers we have counts for
15 papers · 1 filter
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…
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…
Malliavin calculus for signatures with applications to finance
Eduardo Abi Jaber, Clément Rey, Dimitri Sotnikov
Malliavin calculus is a powerful and general framework for the analysis of square-integrable random variables, but it often suffers from a lack of tractability and explicit represe…
Stochastic invariance in infinite dimension beyond Lipschitz coefficients
Eduardo Abi Jaber, Stefan Tappe
We establish necessary and sufficient conditions for stochastic invariance of closed subsets in Hilbert spaces for solutions to infinite-dimensional stochastic differential equatio…
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…
Exponentially Fading Memory Signature
Eduardo Abi Jaber, Dimitri Sotnikov
We introduce the exponentially fading memory (EFM) signature, a time-invariant transformation of an infinite (possibly rough) path that serves as a mean-reverting analogue of the c…