Nicolas Privault

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,

Stochastic analysis in discrete and continuous settings : with normal martingales

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

Chaotic and variational calculus in discrete and continuous time for the poisson process

is the (generalized) Malliavin derivative,

Computations of Greeks in a market with jumps via the Malliavin calculus

\diamond

Performance Analysis of Ambient RF Energy Harvesting with Repulsive Point Process Modeling

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

Stochastic analysis of Bernoulli processes

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

Performance analysis of ambient RF energy harvesting: A stochastic geometry approach

, where

Stein estimation for the drift of Gaussian processes using the Malliavin calculus

{\cal G}^*

Performance analysis of simultaneous wireless information and power transfer with ambient RF energy harvesting

is a space of stochastic distributions and

Self-Sustainable Communications With RF Energy Harvesting: Ginibre Point Process Modeling and Analysis

\mu