Path dependence is omnipresent in social science, engineering, and finance. It reflects the influence of the past on the future, often expressed through functionals. In this talk, we shed light on expansions of functionals. First, we treat static expansions made around paths of fixed length and propose a generalization of the Wiener series − the intrinsic value expansion (IVE). Second, we revisit the functional Taylor expansion (FTE). The latter connects the functional Itô calculus with the signature to quantify the effect in a functional when a "perturbation" path is concatenated with the source path. In particular, the FTE elegantly separates the functional from future trajectories. Lastly, we compare the FTE with the Wiener chaos and show financial applications.
This is joint work with Bruno Dupire (Bloomberg LP).
Valentin Tissot-Daguette is a PhD candidate in the Operations Research and Financial Engineering (ORFE) department at Princeton University supervised by Prof. Mete Soner. Valentin is also a Bloomberg Quantitative Finance PhD Fellow for the 2022-2023 academic year, working with Bruno Dupire.
Prior to his PhD program, Valentin studied at EPFL (Switzerland) where he completed a Bachelor's degree in Mathematics in 2017 and a Master's degree in Financial Engineering in 2020.
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