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Preprints, Working Papers, ... Year : 2024

Path-dependent processes from signatures

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 and open the door to straightforward and simple approximation schemes, that we illustrate numerically.
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Dates and versions

hal-04637402 , version 1 (06-07-2024)

Identifiers

  • HAL Id : hal-04637402 , version 1

Cite

Eduardo Abi Jaber, Louis-Amand Gérard, Yuxing Huang. Path-dependent processes from signatures. 2024. ⟨hal-04637402⟩
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