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
General
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