Fractional smoothness and applications in Finance

Stefan Geiss (1) , Emmanuel Gobet (2)

1 Department of Mathematics [Innsbruck]
2 MATHFI - Mathématiques financières

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.

Mots clés: Fractional smoothness; Discrete time hedging; Interpolation

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Stefan Geiss, Emmanuel Gobet. Fractional smoothness and applications in Finance. Giulia Di Nunno and Bernt Øksendal. Advanced Mathematical Methods for Finance, Springer, pp.313-331, 2011, 978-3-642-18411-6. ⟨10.1007/978-3-642-18412-3_12⟩. ⟨hal-00474803⟩