Convex Duality And Financial Mathematics
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Convex Duality And Financial Mathematics
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Author : Peter Carr
language : en
Publisher: Springer
Release Date : 2018-07-18
Convex Duality And Financial Mathematics written by Peter Carr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-18 with Mathematics categories.
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
Convex Analysis And Variational Problems
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Author : Ivar Ekeland
language : en
Publisher: SIAM
Release Date : 1999-12-01
Convex Analysis And Variational Problems written by Ivar Ekeland and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.
This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
Conjugate Duality And Optimization
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Author : R. Tyrrell Rockafellar
language : en
Publisher: SIAM
Release Date : 1974-01-01
Conjugate Duality And Optimization written by R. Tyrrell Rockafellar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-01-01 with Technology & Engineering categories.
Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.
Lectures On Modern Convex Optimization
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Author : Aharon Ben-Tal
language : fr
Publisher: SIAM
Release Date : 2001-01-01
Lectures On Modern Convex Optimization written by Aharon Ben-Tal and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Technology & Engineering categories.
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Discrete Convex Analysis
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Author : Kazuo Murota
language : en
Publisher: SIAM
Release Date : 2003-01-01
Discrete Convex Analysis written by Kazuo Murota and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.
Convex Stochastic Optimization
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Author : Teemu Pennanen
language : en
Publisher: Springer Nature
Release Date : 2024-12-18
Convex Stochastic Optimization written by Teemu Pennanen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-18 with Mathematics categories.
This book studies a general class of convex stochastic optimization (CSO) problems that unifies many common problem formulations from operations research, financial mathematics and stochastic optimal control. We extend the theory of dynamic programming and convex duality to allow for a unified and simplified treatment of various special problem classes found in the literature. The extensions allow also for significant generalizations to existing problem formulations. Both dynamic programming and duality have played crucial roles in the development of various optimality conditions and numerical techniques for the solution of convex stochastic optimization problems.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Introducing Financial Mathematics
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Author : Mladen Victor Wickerhauser
language : en
Publisher: CRC Press
Release Date : 2022-11-09
Introducing Financial Mathematics written by Mladen Victor Wickerhauser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-09 with Mathematics categories.
Introducing Financial Mathematics: Theory, Binomial Models, and Applications seeks to replace existing books with a rigorous stand-alone text that covers fewer examples in greater detail with more proofs. The book uses the fundamental theorem of asset pricing as an introduction to linear algebra and convex analysis. It also provides example computer programs, mainly Octave/MATLAB functions but also spreadsheets and Macsyma scripts, with which students may experiment on real data.The text's unique coverage is in its contemporary combination of discrete and continuous models to compute implied volatility and fit models to market data. The goal is to bridge the large gaps among nonmathematical finance texts, purely theoretical economics texts, and specific software-focused engineering texts.
The Financial Mathematics Of Market Liquidity
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Author : Olivier Gueant
language : en
Publisher: CRC Press
Release Date : 2016-03-30
The Financial Mathematics Of Market Liquidity written by Olivier Gueant and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Business & Economics categories.
This book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problems-inspired from the Almgren-Chriss app