Eduardo Abi Jaber

Abstract

We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear Volterra and delay equations and in particular the fractional Brownian motion with a Hurst index $H \in (0,1) $. Our expressions allow to disentangle an infinite dimensional Markovian structure. In addition, they open the door to: (i) straightforward and simple approximation schemes that we illustrate numerically, (ii) representations of certain Fourier-Laplace transforms in terms of a non-standard infinite dimensional Riccati equation with important applications for pricing and hedging in quantitative finance.

This is based on joint works with Louis-Amand Gérard and Yuxing Huang.

Our speaker

Eduardo Abi Jaber is an assistant professor (tenure track) in applied mathematics at Ecole Polytechnique. 

He defended his Habilitation à Diriger des Recherches in 2024 and completed his PhD in 2018. 

His research focuses on the role of memory in quantitative finance, with a strong emphasis on mathematical tools such as Volterra processes and path-signatures and their applications to volatility modeling and trading. Bridging the gap between practitioners and academics, his work balances data-driven approaches, advanced modeling techniques, efficient numerical methods and mathematical analysis.  

He has authored more than 25 papers published in peer-reviewed journals in quantitative finance and applied probability. His contributions have been recognized with several awards, including the Amies Prize for the best PhD thesis in applied mathematics (2019) and the Junior Scholar Award of the Bachelier Finance Society (2018).

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