**Date & Time:** Tuesday, September 30, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Martingale Representation Theorems: An Introduction

**Speaker:** B. Rajeev, ISI Bangalore

**Abstract:** At one level, `martingale representation theorems' are the stochastic
analogues of the fundamental theorem of calculus, with the Lebesgue integral
replaced by the Ito integral. Given a functional of a stochastic process like
Brownian motion or Poisson process, it was known that one could represent it as
an Ito integral (a martingale). The problem is to calculate the integrand (the
derivative). This (seemingly obscure) mathematical problem was given a new lease
of life by two subjects: The `stochastic calculus of variations' and `stochastic
finance'. The former introduced a notion of `stochastic derivative' by means of
which one could calculate the integrand and the latter provided applications. In
this talk, we present a notion of `adapted derivative' that can be used to
compute the integrands.