MPS-RR 1998-30
November 1998

White noise generalizations of the Clark-Ocone theorem with application to mathematical finance

by:

Knut Aase, Bernt Øksendal, Jan Ubøe

Abstract

We use a white noise approach to Malliavin calculus to prove a white noise generalization of the Clark-Ocone formula.

We also establish similar results for multidimensional Gaussian white noise, for multidimensional Poissonian white noise and for combined Gaussian and Poissonian noise. Finally we give an application to mathematical finance: We compute the replicating portfolio for a European call option in a Poissonian Black & Scholes type market

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This paper has now been published in Finance Stoch. 4 (2000), no. 4, 465--496