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The Resource Convex duality and financial mathematics, Peter Carr, Qiji Jim Zhu

Convex duality and financial mathematics, Peter Carr, Qiji Jim Zhu

Label
Convex duality and financial mathematics
Title
Convex duality and financial mathematics
Statement of responsibility
Peter Carr, Qiji Jim Zhu
Creator
Contributor
Author
Subject
Language
eng
Summary
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.--
Member of
Assigning source
Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorDate
1958-
http://library.link/vocab/creatorName
Carr, Peter
Dewey number
650.01/51
Index
index present
LC call number
HF5691
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Zhu, Qiji J.
Series statement
SpringerBriefs in mathematics,
http://library.link/vocab/subjectName
  • Business mathematics
  • Convex functions
  • Duality theory (Mathematics)
Label
Convex duality and financial mathematics, Peter Carr, Qiji Jim Zhu
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Contents; 1 Convex Duality; 1.1 Convex Sets and Functions; 1.1.1 Definitions; 1.1.2 Convex Programming; 1.2 Subdifferential and Lagrange Multiplier; 1.2.1 Definition; 1.2.2 Nonemptiness of Subdifferential; 1.2.3 Calculus; 1.2.4 Role in Convex Programming; 1.3 Fenchel Conjugate; 1.3.1 The Fenchel Conjugate; 1.3.2 The Fenchel-Young Inequality; 1.3.3 Graphic Illustration and Generalizations; 1.4 Convex Duality Theory; 1.4.1 Rockafellar Duality; 1.4.2 Fenchel Duality; 1.4.3 Lagrange Duality; 1.4.4 Generalized Fenchel-Young Inequality; Multidimensional Fenchel-Young Inequality
  • 1.5 Generalized Convexity, Conjugacy and DualityRockafellar Duality; Lagrange Duality; 2 Financial Models in One Period Economy; 2.1 Portfolio; 2.1.1 Markowitz Portfolio; 2.1.2 Capital Asset Pricing Model; 2.1.3 Sharpe Ratio; 2.2 Utility Functions; 2.2.1 Utility Functions; 2.2.2 Measuring Risk Aversion; 2.2.3 Growth Optimal Portfolio Theory; 2.2.4 Efficiency Index; 2.3 Fundamental Theorem of Asset Pricing; 2.3.1 Fundamental Theorem of Asset Pricing; 2.3.2 Pricing Contingent Claims; 2.3.3 Complete Market; 2.3.4 Use Linear Programming Duality; 2.4 Risk Measures; 2.4.1 Coherent Risk Measure
  • 2.4.2 Equivalent Characterization of Coherent Risk MeasuresDual Representation; Coherent Acceptance Cone; Coherent Preference; Valuation Bounds and Price System; 2.4.3 Good Deal; 2.4.4 Several Commonly Used Risk Measures; Standard Deviation; Drawdown; Value at Risk; Conditional Value at Risk; Estimating CVaR; 3 Finite Period Financial Models; 3.1 The Model; 3.1.1 An Example; 3.1.2 A General Model; 3.2 Arbitrage and Admissible Trading Strategies; 3.3 Fundamental Theorem of Asset Pricing; 3.3.1 Fundamental Theorem of Asset Pricing
  • 3.3.2 Relationship Between Dual of Portfolio Utility Maximization, Lagrange Multiplier and MartingaleMeasure3.3.3 Pricing Contingent Claims; 3.3.4 Complete Market; 3.4 Hedging and Super Hedging; 3.4.1 Super- and Sub-hedging Bounds; 3.4.2 Towards a Complete Market; 3.4.3 Incomplete Market Arise from Complete Markets; 3.5 Conic Finance; 3.5.1 Modeling Financial Markets with an Ask-Bid Spread; 3.5.2 Characterization of No Arbitrage by Utility Optimization; 3.5.3 Dual Characterization of No Arbitrage; 3.5.4 Pricing and Hedging; 4 Continuous Financial Models; 4.1 Continuous Stochastic Processes
  • 4.1.1 Brownian Motion and Martingale4.1.2 The Itô Formula; Itô Processes; The Multidimensional Itô Formula; Martingale Representation; Dual Itô Formula; 4.1.3 Girsanov Theorem; 4.2 Bachelier and Black-Scholes Formulae; 4.2.1 Pricing Contingent Claims; Bachelier Formula; Black-Scholes Formula; 4.2.2 Convexity; 4.2.3 Duality; 4.3 Duality and Delta Hedging; 4.3.1 Delta Hedging; 4.3.2 Duality; 4.3.3 Time Reversal; 4.4 Generalized Duality and Hedging with Contingent Claims; 4.4.1 Preservation of Generalized Convexity in the Value Function of a Contingent Claim; Consistency of Generalized Convexity
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319924915
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1045796474
  • (OCoLC)1045796474
Label
Convex duality and financial mathematics, Peter Carr, Qiji Jim Zhu
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Contents; 1 Convex Duality; 1.1 Convex Sets and Functions; 1.1.1 Definitions; 1.1.2 Convex Programming; 1.2 Subdifferential and Lagrange Multiplier; 1.2.1 Definition; 1.2.2 Nonemptiness of Subdifferential; 1.2.3 Calculus; 1.2.4 Role in Convex Programming; 1.3 Fenchel Conjugate; 1.3.1 The Fenchel Conjugate; 1.3.2 The Fenchel-Young Inequality; 1.3.3 Graphic Illustration and Generalizations; 1.4 Convex Duality Theory; 1.4.1 Rockafellar Duality; 1.4.2 Fenchel Duality; 1.4.3 Lagrange Duality; 1.4.4 Generalized Fenchel-Young Inequality; Multidimensional Fenchel-Young Inequality
  • 1.5 Generalized Convexity, Conjugacy and DualityRockafellar Duality; Lagrange Duality; 2 Financial Models in One Period Economy; 2.1 Portfolio; 2.1.1 Markowitz Portfolio; 2.1.2 Capital Asset Pricing Model; 2.1.3 Sharpe Ratio; 2.2 Utility Functions; 2.2.1 Utility Functions; 2.2.2 Measuring Risk Aversion; 2.2.3 Growth Optimal Portfolio Theory; 2.2.4 Efficiency Index; 2.3 Fundamental Theorem of Asset Pricing; 2.3.1 Fundamental Theorem of Asset Pricing; 2.3.2 Pricing Contingent Claims; 2.3.3 Complete Market; 2.3.4 Use Linear Programming Duality; 2.4 Risk Measures; 2.4.1 Coherent Risk Measure
  • 2.4.2 Equivalent Characterization of Coherent Risk MeasuresDual Representation; Coherent Acceptance Cone; Coherent Preference; Valuation Bounds and Price System; 2.4.3 Good Deal; 2.4.4 Several Commonly Used Risk Measures; Standard Deviation; Drawdown; Value at Risk; Conditional Value at Risk; Estimating CVaR; 3 Finite Period Financial Models; 3.1 The Model; 3.1.1 An Example; 3.1.2 A General Model; 3.2 Arbitrage and Admissible Trading Strategies; 3.3 Fundamental Theorem of Asset Pricing; 3.3.1 Fundamental Theorem of Asset Pricing
  • 3.3.2 Relationship Between Dual of Portfolio Utility Maximization, Lagrange Multiplier and MartingaleMeasure3.3.3 Pricing Contingent Claims; 3.3.4 Complete Market; 3.4 Hedging and Super Hedging; 3.4.1 Super- and Sub-hedging Bounds; 3.4.2 Towards a Complete Market; 3.4.3 Incomplete Market Arise from Complete Markets; 3.5 Conic Finance; 3.5.1 Modeling Financial Markets with an Ask-Bid Spread; 3.5.2 Characterization of No Arbitrage by Utility Optimization; 3.5.3 Dual Characterization of No Arbitrage; 3.5.4 Pricing and Hedging; 4 Continuous Financial Models; 4.1 Continuous Stochastic Processes
  • 4.1.1 Brownian Motion and Martingale4.1.2 The Itô Formula; Itô Processes; The Multidimensional Itô Formula; Martingale Representation; Dual Itô Formula; 4.1.3 Girsanov Theorem; 4.2 Bachelier and Black-Scholes Formulae; 4.2.1 Pricing Contingent Claims; Bachelier Formula; Black-Scholes Formula; 4.2.2 Convexity; 4.2.3 Duality; 4.3 Duality and Delta Hedging; 4.3.1 Delta Hedging; 4.3.2 Duality; 4.3.3 Time Reversal; 4.4 Generalized Duality and Hedging with Contingent Claims; 4.4.1 Preservation of Generalized Convexity in the Value Function of a Contingent Claim; Consistency of Generalized Convexity
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319924915
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1045796474
  • (OCoLC)1045796474

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