The Interval Market Model in Mathematical Finance

Game-Theoretic Methods

  • Pierre Bernhard
  • Jacob C. Engwerda
  • Berend Roorda
  • J.M. Schumacher
  • Vassili Kolokoltsov
  • Patrick Saint-Pierre
  • Jean-Pierre Aubin

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Revisiting Two Classic Results in Dynamic Portfolio Management

    1. Front Matter
      Pages 1-2
    2. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 3-16
    3. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 17-26
  3. Hedging in Interval Models

    1. Front Matter
      Pages 27-29
    2. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 31-44
    3. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 45-63
    4. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 65-77
    5. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 79-86
  4. Robust-Control Approach to Option Pricing

    1. Front Matter
      Pages 87-90
    2. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 91-105
    3. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 107-165
    4. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 167-197
    5. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 199-213
  5. Game-Theoretic Analysis of Rainbow Options in Incomplete Markets

    1. Front Matter
      Pages 215-215
    2. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 217-219
    3. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 221-247
    4. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 249-260
    5. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 261-272
    6. Pierre Bernhard, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre et al.
      Pages 273-283

About this book

Introduction

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods.

A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including:

·         probability-free Black-Scholes theory;

·         fair-price interval of an option;

·         representation formulas and fast algorithms for option pricing;

·         rainbow options;

·         tychastic approach of mathematical finance based upon viability theory.

This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.

Keywords

Hamilton-Jacobi-Belman equation Isaacs equation dynamic programming financial mathematics game theory interval market model option pricing robust control

Authors and affiliations

  • Pierre Bernhard
    • 1
  • Jacob C. Engwerda
    • 2
  • Berend Roorda
    • 3
  • J.M. Schumacher
    • 4
  • Vassili Kolokoltsov
    • 5
  • Patrick Saint-Pierre
    • 6
  • Jean-Pierre Aubin
    • 7
  1. 1.INRIA Sophia Antipolis-MediterraneeSophia Antipolis cedexFrance
  2. 2.School of Economics and Management, Econometrics and Operations ResearchTilburg UniversityTilburgNetherlands
  3. 3., Department of Industrial EngineeringUniversity of TwenteEnschedeNetherlands
  4. 4., Econometrics and Operations ResearchTilburg UniversityTilburgNetherlands
  5. 5., Department of StatisticsUniversity of WarwickWarwickUnited Kingdom
  6. 6.Université Paris DauphineParis Cedex 16France
  7. 7.VIMADESParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8388-7
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8387-0
  • Online ISBN 978-0-8176-8388-7
  • About this book