Convex Duality and Financial Mathematics
Department
Mathematics
Document Type
Book
Files
Description
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.
Call number in WMU's library
HF5691 .C377 2018 (Waldo Library, WMU Authors Collection, First Floor)
ISBN
978-3-319-92491-5
Publication Date
7-2018
Keywords
Convex duality, Fenchel conjugate, utility function, risk measures, arbitrage, martingale measure, asset pricing, hedging, financial derivatives, Lagrange multipliers, financial market, quantitative finance
Disciplines
Mathematics
Recommended Citation
Carr, Peter and Zhu, Qiji Jim, "Convex Duality and Financial Mathematics" (2018). All Books and Monographs by WMU Authors. 841.
https://scholarworks.wmich.edu/books/841