A note on functional derivatives on continuous paths

Shaolin Ji and Shuzhen Yang

Statistics & Probability Letters, 2015, vol. 106, issue C, 176-183

Abstract: In this paper, we study the relation between Fréchet derivatives, Dupire derivatives in Dupire (2009) and the derivatives modified by Levental et al. (2010). After introducing the definition of Fréchet derivatives for non-anticipative functionals, we prove that the Dupire derivatives, the extended Fréchet derivatives and the new setup in Levental et al. (2010) are coherent on continuous paths.

Keywords: Dupire derivatives; Functional Itô’s calculus; Backward stochastic differential equations; Path-dependent PDEs; Fréchet derivatives (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.07.024

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