Generalised small-noise expansion for projected diffusions and applications

Monday 23rd January 2012 – 15:45 to 16:45

Speaker: Antoine Jacquier (Imperial College, London)

Given a diffusion in Rn, we prove a small-noise expansion for the density of its projection on a subspace of dimension p (p≤n). Our proof relies on the Laplace method on Wiener space and stochastic Taylor expansions in the spirit of Azencott-Benarous-Bismut. Our result (assuming Hormander’s condition on the vector fields) applies both (i) to small-time asymptotics and (ii) to the tails of the distribution. In the context of stochastic volatility models, we recover the Busca-Berestycki-Florent formula (applying (i)) and Gulisashvili-Stein expansion (from (ii)).