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Convex Duality and Financial Mathematics

  • Book
  • © 2018

Overview

Authors:
  1. Peter Carr

    1. Department of Finance and Risk Engineering, Tandon School of Engineering, New York University, New York, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Qiji Jim Zhu

    1. Department of Mathematics, Western Michigan University, Kalamazoo, USA

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    You can also search for this author in PubMed   Google Scholar

  • Emphasizes a heuristic understanding of convex duality in financial mathematics
  • Introduces arbitrage pricing, utility maximization, and risk measures via convex duality
  • Provides real-world financial applications

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Convex Duality

    • Peter Carr, Qiji Jim Zhu
    Pages 1-33

  3. Financial Models in One Period Economy

    • Peter Carr, Qiji Jim Zhu
    Pages 35-82

  4. Finite Period Financial Models

    • Peter Carr, Qiji Jim Zhu
    Pages 83-106

  5. Continuous Financial Models

    • Peter Carr, Qiji Jim Zhu
    Pages 107-140

  6. Back Matter

    Pages 141-152
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Keywords

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 itsrelationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims

Reviews

“This comprehensive work is prepared in a thoughtful way, rigorously and well-organized. … This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. … This excellent book is very well embedded into the scientific landscapes of both financial mathematics and convex optimization, including numerous future potentials, very well exemplified and illustrated, and very well written.” (Gerhard-Wilhelm Weber, zbMath 1416.91003, 2019)

Authors and Affiliations

  • Department of Finance and Risk Engineering, Tandon School of Engineering, New York University, New York, USA

    Peter Carr

  • Department of Mathematics, Western Michigan University, Kalamazoo, USA

    Qiji Jim Zhu

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