Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

The classical Ito stochastic representation theorem asserts that any square integrable random variable, which is a functional of the Brownian motion, can be expressed as a stochastic integral plus its expectation. Clark-Ocone representation formula provides an explicit expression for this integral representation in terms of the derivative in the sense of Malliavin calculus. We will compare this formula with the classical Ito formula and we will discuss its application in hedging contingent claims in finance. In the second part of the talk we present a recent proof of a central limit theorem for the modulus of continuity in the space variable of the Brownian local time, based on Clark-Ocone formula.

Speaker: David Nualart, University of Kansas

Slides: (TBA)