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arXiv · 2407.04956

Path-dependent processes from signatures

Eduardo Abi Jaber·Louis-Amand Gérard·Yuxing Huang
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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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Eduardo Abi Jaber, Louis-Amand Gérard, Yuxing Huang. 2024-07-06. Path-dependent processes from signatures. https://arxiv.org/abs/2407.04956

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