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Convex Duality And Financial Mathematics
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Book Synopsis Convex Duality and Financial Mathematics by : Peter Carr
Download or read book Convex Duality and Financial Mathematics written by Peter Carr and published by Springer. This book was released on 2018-07-18 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Duality in Mathematical Finance by : Marco Frittelli
Download or read book Duality in Mathematical Finance written by Marco Frittelli and published by Springer. This book was released on 2007 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an advanced and unified treatment of four important issues that have dominated the theoretical research in mathematical finance for the last ten years: (1) the fundamental theorem of asset pricing; (2) utility maximization in incomplete markets; (3) pricing in incomplete markets; (4) the risk measurement of a static payoff and of a cash-flow stream. The powerful tools of convex analysis and duality theory are systematically applied to investigate these topics, under very general assumptions on the financial markets. This duality approach reveals the prominent role of the investor’s preferences in all these fundamental issues and contributes to a deeper understanding of the economic aspects of the theory.
Book Synopsis Convex Analysis and Variational Problems by : Ivar Ekeland
Download or read book Convex Analysis and Variational Problems written by Ivar Ekeland and published by SIAM. This book was released on 1999-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Conjugate Duality and Optimization by : R. Tyrrell Rockafellar
Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Modern Convex Optimization by : Aharon Ben-Tal
Download or read book Lectures on Modern Convex Optimization written by Aharon Ben-Tal and published by SIAM. This book was released on 2001-01-01 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of Convex Analysis and Optimization by : Rafael Correa
Download or read book Fundamentals of Convex Analysis and Optimization written by Rafael Correa and published by Springer Nature. This book was released on 2023-07-11 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.
Book Synopsis Discrete Convex Analysis by : Kazuo Murota
Download or read book Discrete Convex Analysis written by Kazuo Murota and published by SIAM. This book was released on 2003-01-01 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Preinvexity and Second Order Duality in Multiobjective Programming by : Xinmin Yang
Download or read book Generalized Preinvexity and Second Order Duality in Multiobjective Programming written by Xinmin Yang and published by Springer. This book was released on 2018-09-27 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to several new generalized preinvex functions and generalized invariant monotone functions. It begins by describing the main properties of these functions and various relations. Several examples are then presented to illustrate various interesting relationships among preinvex functions and the properly inclusive relations among the generalized invariant monotonicities. In addition, several second order and higher order symmetric duality models are provided for multi-objective nonlinear programming problems. Lastly, weak and strong duality theorems under generalized convexity assumptions are provided. The book offers a well-synthesized, accessible, and usable treatment for students, researchers and practitioners in the areas of OR, optimization, applied mathematics and engineering, and all those working on a wide range of related problems, which include financial institutions, logistics, transportation, traffic management, etc.
Book Synopsis Interior-point Polynomial Algorithms in Convex Programming by : Yurii Nesterov
Download or read book Interior-point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Book Synopsis Convex Optimization by : Stephen P. Boyd
Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Mathematical View of Interior-point Methods in Convex Optimization by : James Renegar
Download or read book A Mathematical View of Interior-point Methods in Convex Optimization written by James Renegar and published by SIAM. This book was released on 2001-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Book Synopsis Stochastic Processes and Financial Mathematics by : Ludger Rüschendorf
Download or read book Stochastic Processes and Financial Mathematics written by Ludger Rüschendorf and published by Springer Nature. This book was released on 2023-04-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while at the same time placing much emphasis on good readability, motivation, and explanation of the issues covered. Financial mathematical topics are first introduced in the context of discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central results of stochastic analysis such as the Itô formula, Girsanov's theorem and martingale representation theorems are of fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of topics. Advanced knowledge of probability theory is assumed, in particular of discrete-time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, Lévy processes, processes with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading and for instructors as a basis for their own courses. This book is a translation of the original German 1st edition Stochastische Prozesse und Finanzmathematik by Ludger Rüschendorf, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Book Synopsis An Easy Path to Convex Analysis and Applications by : Boris S. Mordukhovich
Download or read book An Easy Path to Convex Analysis and Applications written by Boris S. Mordukhovich and published by Morgan & Claypool Publishers. This book was released on 2013-12-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical f
Book Synopsis Scalar and Vector Risk in the General Framework of Portfolio Theory by : Stanislaus Maier-Paape
Download or read book Scalar and Vector Risk in the General Framework of Portfolio Theory written by Stanislaus Maier-Paape and published by Springer Nature. This book was released on 2023-09-01 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the culmination of the authors’ industry-academic collaboration in the past several years. The investigation is largely motivated by bank balance sheet management problems. The main difference between a bank balance sheet management problem and a typical portfolio optimization problem is that the former involves multiple risks. The related theoretical investigation leads to a significant extension of the scope of portfolio theories. The book combines practitioners’ perspectives and mathematical rigor. For example, to guide the bank managers to trade off different Pareto efficient points, the topological structure of the Pareto efficient set is carefully analyzed. Moreover, on top of computing solutions, the authors focus the investigation on the qualitative properties of those solutions and their financial meanings. These relations, such as the role of duality, are most useful in helping bank managers to communicate their decisions to the different stakeholders. Finally, bank balance sheet management problems of varying levels of complexity are discussed to illustrate how to apply the central mathematical results. Although the primary motivation and application examples in this book are focused in the area of bank balance sheet management problems, the range of applications of the general portfolio theory is much wider. As a matter of fact, most financial problems involve multiple types of risks. Thus, the book is a good reference for financial practitioners in general and students who are interested in financial applications. This book can also serve as a nice example of a case study for applied mathematicians who are interested in engaging in industry-academic collaboration.
Book Synopsis Optimization by Vector Space Methods by : David G. Luenberger
Download or read book Optimization by Vector Space Methods written by David G. Luenberger and published by John Wiley & Sons. This book was released on 1997-01-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Book Synopsis Advanced Mathematical Methods for Finance by : Julia Di Nunno
Download or read book Advanced Mathematical Methods for Finance written by Julia Di Nunno and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.
