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. Föllmer, F. Baudoin, L.C.G. Rogers, and M. Soner/N. Touzi.

M.H. Soner, N. Touzi: The Problem of Super-replication under Constraints.- F. Baudoin: Modelling Anticipations on Financial Markets.- L.C.G. Rogers: Duality in Constrained Optimal Investment and Consumption problems: A Synthesis.- P. Bank, H. Föllmer: American Options, Multi-armed Bandits, and Optimal Consumption Plans: A Unifying View.