Convex Duality and Financial Mathematics

  • Peter Carr
  • Qiji Jim Zhu

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Peter Carr, Qiji Jim Zhu
    Pages 1-33
  3. Peter Carr, Qiji Jim Zhu
    Pages 35-82
  4. Peter Carr, Qiji Jim Zhu
    Pages 83-106
  5. Peter Carr, Qiji Jim Zhu
    Pages 107-140
  6. Back Matter
    Pages 141-152

About this book


This book provides a  concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization.

Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims


Convex duality Fenchel conjugate utility function risk measures arbitrage martingale measure asset pricing hedging financial derivatives Lagrange multipliers financial market

Authors and affiliations

  • Peter Carr
    • 1
  • Qiji Jim Zhu
    • 2
  1. 1.Department of Finance and Risk EngineeringTandon School of Engineering, New York UniversityNew YorkUSA
  2. 2.Department of MathematicsWestern Michigan UniversityKalamazooUSA

Bibliographic information