4 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…
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…
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…
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…