Optimisation et contrôle stochastique appliqués à la finance / Edition 1

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Overview

L'objectif et l'originalité de ce livre est de présenter les différents aspects et méthodes utilise's dans la résolution des problèmes d'optimisation shastique 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 intéresse's par l'optimisation et le contrôle shastique applique's à la finance.

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Editorial Reviews

From the Publisher
From the reviews:

"This book concerns postgraduate studies in shastic analysis, especially optimal shastic control. The presentation is pedagogic and progressive. It stresses the links between shastic differential equations (SDEs), dynamic programming and viscosity solutions. … There are six chapters. … The references are numerous (61) and widely commented on at the end of each chapter. An alphabetic index ends the book." (Monique Pontier, Mathematical reviews, Issue 2008 g)

"The book is an original presentation of classical and recent techniques for shastic control problems and their applications in mathematical finance. … I consider this book a very useful tool for students and researchers who want to reach rapidly an adequate knowledge of modern techniques in shastic control to be able to enter the recent literature concerning the applications of shastic control methods to mathematical finance." (Giovanni Di Masi, Zentralblatt MATH, Vol. 1143, 2008)

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Product Details

  • ISBN-13: 9783540737360
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 9/6/2007
  • Language: French
  • Series: Mathematiques et Applications Series , #61
  • Edition description: 2007
  • Edition number: 1
  • Pages: 188
  • Product dimensions: 0.44 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Quelques éléments d'analyse shastique.- Prob&lgrave;emes d'optimisation shastique. Exemples en finance.- Approche EDP classique de la programmation dynamique.- Approche des équations de Bellman par les solutions de viscosité.- Méthodes d'équations différentielles shastiques rétrogrades.- Méthodes martingales de dualité convexe.

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