Jan Ubøe

White Noise Generalizations of the Clark-Haussmann-Ocone Theorem with Application to Mathematical Finance

Abstract. We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula \[F(\omega)=E[F]+\int_0^TE[D_tF|\F_t]\diamond W(t)dt\] Here E[F] denotes the generalized expectation,

The burgers equation with a noisy force and the stochastic heat equation

D_tF(\omega)={{dF}\over{d\omega}}

A maximum entropy approach to the newsvendor problem with partial information

is the (generalized) Malliavin derivative,

Using the Donsker Delta Function to Compute Hedging Strategies

\diamond

The Pressure Equation for Fluid Flow in a Stochastic Medium

is the Wick product and W(t) is 1-dimensional Gaussian white noise. The formula holds for all

Stochastic boundary value problems. A white noise functional approach.

f\in{\cal G}^*\supset L^2(\mu)

Aggregation of gravity models for journeys to work

, where

A Network Approach to Commuting

{\cal G}^*

Replication/Prediction Problems in the Journey to Work

is a space of stochastic distributions and

Discrete wick calculus and stochastic functional equations

\mu