A generalized Clark-Ocone formula

An extension of the Clark-Ocone formula

A Clark-ocone Formula in Umd Banach Spaces

Let H be a separable real Hilbert space and let F = (Ft)t∈[0,T ] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T ] on a probability space (Ω,F ,P). We prove that if E is a UMD Banach space, 1 ≤ p < ∞, and F ∈ D(Ω;E) is FT -measurable, then F = E(F ) + ∫ T 0 PF(DF ) dWH , where D is the Malliavin derivative of F and PF is the projection onto the F-adapted ...

Hedging in bond markets by the Clark-Ocone formula

Hedging strategies in bond markets are computed by martingale representation and the choice of a suitable of numeraire, based on the Clark-Ocone formula in a model driven by the dynamics of bond prices. Applications are given to the hedging of swaptions and other interest rate derivatives and we compare our approach to delta hedging when the underlying swap rate is modeled by a diffusion process.

Generalised Clark-ocone Formulae for Differential Forms

We generalise the Clark-Ocone formula for functions to give analogous representations for differential forms on the classical Wiener space. Such formulae provide explicit expressions for closed and co-closed differential forms and, as a by-product, a new proof of the triviality of the L de Rham cohomology groups on the Wiener space, alternative to Shigekawa’s approach [15] and the chaos-theoret...

– Ocone Formula and Poisson Functionals

In this paper we first prove a Clark–Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational representation formula for the Laplace transform of bounded Poisson functionals, which has been conjectured by Dupuis and Ellis [A Weak Convergence Approach to the Theo...