_________________________________________________________________________ SOME FUNDAMENTAL THEOREMS IN MATHEMATICAL FINANCE: A STOCHASTIC PROGRAMMING DUALITY PERSPECTIVE _________________________________________________________________________ Lisa A. Korf Department of Mathematics University of Washington, Seattle Date. Tuesday, 6th of June 2000 ------------------------- Time. 16.30 ----- Location. Seminarraum 107, 6th floor, green area, TU WIEN - Freihaus -------------------------- ------- Abstract. Stochastic programming concerns the theory of making optimal decisions under uncertainty, in which a probability distribution has been assigned to the uncertain parameters of a problem. These are generally optimization problems in infinite-dimensional spaces. Much of the theory revolves around how to approximate such problems in finite dimensions so that they might be solved in a practical mathematical programming setting. In addition, a nice duality theory has been developed in the infinite- dimensional setting. It was only natural that financial applications took their place as one of the primary application areas in this field. Mathematical programming provides a flexible framework in which to model all kinds of stochastic price processes, as well as the unavoidable complications of constraints, costs, etc. which arise in practice. While much attention has been focused on the practical aspects of solving these problems, little attention has been paid to deriving some of the rich (finite and infinite-dimensional) theory of mathematical finance in a stochastic programming duality setting, where extensions to problems with transaction costs, etc. would be considered very natural. This lecture introduces stochastic programming duality, and delves into some of the fascinating issues involved in trying to derive the ``fundamental theorems of asset pricing'' (equating no arbitrage conditions with the existence of an equivalent martingale measure for the underlying asset price process) in a stochastic programming framework. __________________________________________________________________________ Further information about the schedule of seminars at the Department of Financial and Actuarial Mathematics is available at http://www.fam.tuwien.ac.at/schedule ! ------------------------------------