Clark-Ocone formula by the S-transform on the Poisson white noise space

An extension of the Clark-Ocone formula

The Clark-Haussmann-Ocone theorem WHITE NOISE GENERALIZATIONS OF THE CLARK-HAUSSMANN-OCONE THEOREM, WITH APPLICATION TO MATHEMATICAL FINANCE

We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] ⋄ W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative,⋄ is the Wick product and W (t) is 1-dimensional Gaussian white noise. The formula holds for all f ∈ G * ...

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.

– 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...

The Clark–ocone Formula for Vector Valued Random Variables in Abstract Wiener Space

Erratum to " The Clark-Ocone formula for vector valued random variables in abstract Wiener space " , Jour. In this paper we considered the extension of the Clark-Ocone formula for a random variable defined on an abstract Wiener space (W, H, µ) and taking values in a Banach space (denoted there either B or Y). The main result appears in Theorem 3.4. Unfortunately, as first pointed out to us by J...