EAN: 9783319924915

SPRINGERBRIEFS IN MATHEMATICS CONVEX DUALITY ...

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

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