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.