The Paris-Princeton Lectures in Financial Mathematics, of which this is the first volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming - specialists. The aim is to produce a series of articles that can serve as an introductory reference for research in the field. It arises as a result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with articles by P. Bank/H. Follmer, F. Baudoin, L.C.G. Rogers,...