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- W4313305514 abstract "Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often infinite-dimensional, thus challenging from a conceptual and computational perspective. In this work, 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). In the dynamic case, we revisit the functional Taylor expansion (FTE). The latter connects the functional It^o 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. The notions of real analyticity and radius of convergence are also extended to the path space. We discuss other dynamic expansions arising from Hilbert projections and the Wiener chaos, and finally show financial applications of the FTE to the pricing and hedging of exotic contingent claims." @default.
- W4313305514 created "2023-01-06" @default.
- W4313305514 creator A5013056807 @default.
- W4313305514 creator A5060208733 @default.
- W4313305514 date "2022-12-27" @default.
- W4313305514 modified "2023-10-16" @default.
- W4313305514 title "Functional Expansions" @default.
- W4313305514 doi "https://doi.org/10.48550/arxiv.2212.13628" @default.
- W4313305514 hasPublicationYear "2022" @default.
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