Huyên Pham

This is the third volume in "The Paris-Princeton Lectures in Financial Mathematics", which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by Rene Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyen Pham.

L'objectif et l'originalité de ce livre est de présenter les différents aspects et méthodes utilisés dans la résolution des problèmes d'optimisation stochastique avec en vue des applications plus spécifiques à la finance: gestion de portefeuille, couverture d'options, investissement optimal. Nous avons inclus certains développements récents sur le sujet sans chercher a priori la plus grande généralité. Nous avons voulu une exposition graduelle des méthodes mathématiques en présentant d'abord les idées intuitives puis en énonçant précisément les résultats avec des démonstrations complètes et détaillées. Nous avons aussi pris soin d'illustrer chacune des méthodes de résolution sur de nombreux exemples issus de la finance. Nous espérons ainsi que ce livre puisse être utile aussi bien pour des étudiants que pour des chercheurs du monde académique ou professionnel intéressés par l'optimisation et le contrôle stochastique appliqués à la 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 toknow 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 toknow more about the use of stochastic optimization methods in finance.