Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control.

This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc.

This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

L'objectif et l'originalite de ce livre est de presenter les differents aspects et methodes utilises dans la resolution des problemes d'optimisation stochastique avec en vue des applications plus specifiques a la finance: gestion de portefeuille, couverture d'options, investissement optimal.
Nous avons inclus certains developpements recents sur le sujet sans chercher a priori la plus grande generalite. Nous avons voulu une exposition graduelle des methodes mathematiques en presentant d'abord les idees intuitives puis en enoncant precisement les resultats avec des demonstrations completes et detaillees.
Nous avons aussi pris soin d'illustrer chacune des methodes de resolution sur de
nombreux exemples issus de la finance. Nous esperons ainsi que ce livre puisse etre utile aussi bien pour des etudiants que pour des chercheurs du monde academique ou professionnel interesses par l'optimisation et le controle stochastique appliques a la finance.

This book is taken from the lectures given at the ENSAE in March 1998 and at the Scuola Normale Superiore in May 1998. At the beginning of the 70's, the set of mathematical methods of finance were reduced to actuarial calculus. The modern approach uses the stochastic calculus theory and evidences the duality between problems of arbitrage and valorisation and a set of martingale probabilities.