Convex Duality and Financial Mathematics

by Peter Carr, Qiji Jim Zhu

Overview

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

Product Details

ISBN-13:	9783319924915
Publisher:	Springer International Publishing
Publication date:	07/19/2018
Series:	SpringerBriefs in Mathematics
Edition description:	1st ed. 2018
Pages:	152
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

1. Convex Duality.- 2. Financial Models in One Period.- 3. Finite Period Financial Models.- 4. Continuous Financial Models.- References.

Editorial 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)

From the Publisher