Section: New Results

Keywords : Monte-Carlo, variance reduction.

Monte Carlo simulations and stochastic algorithms

Participants : V. Bally, E.H.A. Dia, D. Lamberton, B. Lapeyre, J. Lelong, P. Tankov.

El Hadj Aly Dia is starting a thesis on Monte-Carlo methods for exotic options in models with jumps.

P. Tankov and J. Poirot have submitted a paper on `` Monte–Carlo option pricing for tempered stable (CGMY) processes'' to Asia-Pacific financial markets (following a conference in Kanazawa, Japan)

J. Lelong has worked on the convergence rate of stochastic algorithms truncated at randomly varying bounds. He has proved a functional central limit theorem for these algorithms. He has also considered an averaging version of this algorithm and established a component-wise CLT for it.

V. Bally, L. Caramellino and A. Zanette have developped a mixed PDE - Monte Carlo approach for pricing credit default index swaptions. (see [14] ).

D. Lamberton and Gilles Pagès have studied the rate of convergence of the classical two-armed bandit algorithm. They have also investigated another algorithm with a penalization procedure. Two papers have been sumitted.