The martingale representation theorem is one of the fundamental results in Ito's stochastic calculus and it has been applied to establish the completeness of the Black-Scholes model in finance. An explicit expression for the integrand in this representation, called Clark-Ocone formula, can be obtained in terms of the derivative operator in the sense of Malliavin calculus.

In this talk we will discuss some generalizations of this formula and its applications to compute the hedging portfolio in some particular examples. We will also present the applications of this formula to establish central limit theorems for Brownian local time increments.