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Convex duality and financial mathematics

Carr, Peter.

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Convex duality and financial mathematics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convex duality and financial mathematics/ by Peter Carr, Qiji Jim Zhu.
作者:	Carr, Peter.
其他作者:	Zhu, Qiji Jim.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xiii, 152 p. :digital ;24 cm.
內容註:	1. Convex Duality -- 2. Financial Models in One Period -- 3. Finite Period Financial Models -- 4. Continuous Financial Models -- References.
Contained By:	Springer eBooks
標題:	Business mathematics. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-92492-2
ISBN:	9783319924922

Convex duality and financial mathematics
Carr, Peter.

Convex duality and financial mathematics[electronic resource] /by Peter Carr, Qiji Jim Zhu. - Cham :Springer International Publishing :2018. - xiii, 152 p. :digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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

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.

ISBN: 9783319924922

Standard No.: 10.1007/978-3-319-92492-2doiSubjects--Topical Terms:

625055
Business mathematics.

LC Class. No.: HF5691 / .C377 2018

Dewey Class. No.: 650.0151

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520 $a 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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