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Probability and Computational Finance Seminar
Antoine Jacquier Imperial College (London) Title: Generalised small-noise expansion for projected diffusions and applications Abstract: 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 (i) to small-time asymptotics, (ii) to tails of distributions and (iii) to small perturbation problems. In the context of stochastic volatility models, we recover the Busca-Berestycki-Florent formula (applying (i)) and Gulisashvili-Stein expansion (from (ii)).This is a joint work with J.D. Deuschel (TU Berlin), P. Friz (TU Berlin) and S. Violante (Imperial College London). Date: Monday, March 26, 2012 Time: 5:00 pm Location: Wean Hall 5409 Submitted by: Kasper Larsen |