Probability Seminar Department of Statistics and Department of Mathematics Monday, September 9, 2002 3:30 PM in REC 113 Professor Jin Ma Purdue University will speak on Representations and Regularities for Solutions to BSDEs with Reflections Abstract In this talk I will present some recent results on the fine properties of solutions to Backward Stochastic Differential Equations with Reflections (BSDER). Several issues will be addressed: the Feynman-Kac representation formula for the martingale integrand of the BSDER; the path regularity of the solution (especially that of the martingale integrand); the C1-regularity of the solution to the corresponding variational inequality of PDE; and finally the numerical method for BSDERs. In particular, a new notion of regularity for a stochastic process, called the ``L2-modulus regularity", will be introduced. We show that such regularity of the martingale integrand produces exactly the rate of convergence (in the strong L2-sense!) of the numerical scheme. All these results are based on several different types of discretizations of BSDER in the spirit of the so-called Bermuda Options in finance.

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