Overview
- 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)
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
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Bibliographic Information
Book Title: Convex Duality and Financial Mathematics
Authors: Peter Carr, Qiji Jim Zhu
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-92492-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-92491-5Published: 28 July 2018
eBook ISBN: 978-3-319-92492-2Published: 18 July 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIII, 152
Number of Illustrations: 26 illustrations in colour
Topics: Quantitative Finance, Game Theory, Economics, Social and Behav. Sciences, Operations Research, Management Science, Real Functions