1 citations · 1 across the 6 of their papers we have counts for
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…
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…
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…
Martingale property and moment explosions in signature volatility models
Eduardo Abi Jaber, Paul Gassiat, Dimitri Sotnikov
We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of…
Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration
Eduardo Abi Jaber, Soukaïna Bruneau, Nathan De Carvalho +2
In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlatio…