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Author : Teemu Pennanen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (118 download)
Download or read book Convex Duality in Stochastic Programming and Mathematical Finance written by Teemu Pennanen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter Carr
Publisher : Springer
ISBN 13 : 3319924923
Total Pages : 162 pages
Book Rating : 4.3/5 (199 download)
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
Author : J. Frédéric Bonnans
Publisher : Springer
ISBN 13 : 3030149773
Total Pages : 311 pages
Book Rating : 4.0/5 (31 download)
Download or read book Convex and Stochastic Optimization written by J. Frédéric Bonnans and published by Springer. This book was released on 2019-04-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules. This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.
Author : Willem K. Klein Haneveld
Publisher : Springer Science & Business Media
ISBN 13 : 3642516971
Total Pages : 299 pages
Book Rating : 4.6/5 (425 download)
Download or read book Duality in Stochastic Linear and Dynamic Programming written by Willem K. Klein Haneveld and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 1611973422
Total Pages : 512 pages
Book Rating : 4.6/5 (119 download)
Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2014-07-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available.? In?Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results.?
Author : R. Tyrrell Rockafellar
Publisher : SIAM
ISBN 13 : 9781611970524
Total Pages : 80 pages
Book Rating : 4.9/5 (75 download)
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.
Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 0898718759
Total Pages : 447 pages
Book Rating : 4.8/5 (987 download)
Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2009-01-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
Author : Huyên Pham
Publisher : Springer Science & Business Media
ISBN 13 : 3540895000
Total Pages : 243 pages
Book Rating : 4.5/5 (48 download)
Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
Author : Aaron Xin Situ
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.:/5 (926 download)
Download or read book Convex Stochastic Control and Conjugate Duality in a Problem of Unconstrained Utility Maximization Under a Regime Switching Model written by Aaron Xin Situ and published by . This book was released on 2015 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we examine a problem of convex stochastic optimal control applied to mathematical finance. The goal is to maximize the expected utility from wealth at close of trade (or terminal wealth) under a regime switching model. The presence of regime switching constitutes a definite challenge, and in order to keep the analysis tractable we therefore adopt a market model which is in other respects quite simple, and in particular does not involve margin payments, inter-temporal consumption or portfolio constraints. The asset prices will be modeled by classical Ito processes, and the market parameters will be dependent on the underlying Brownian Motion as well as a finite-state Markov Chain which represents the "regime switching" aspect of the market model. We use conjugate duality to construct a dual optimization problem and establish optimality relations between (putative) solutions of the dual and primal problems. We then apply these optimality relations to two specific types of utility functions, namely the power utility and logarithmic utility functions, and for these utility functions we obtain the optimal portfolios in completely explicit and implementable form.
Author : Manfred Walk
Publisher : Springer
ISBN 13 :
Total Pages : 186 pages
Book Rating : 4.:/5 (44 download)
Download or read book Theory of Duality in Mathematical Programming written by Manfred Walk and published by Springer. This book was released on 1989 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Liao Heng
Publisher : Cambridge University Press
ISBN 13 : 1316513580
Total Pages : 399 pages
Book Rating : 4.3/5 (165 download)
Download or read book Mathematics for Future Computing and Communications written by Liao Heng and published by Cambridge University Press. This book was released on 2021-12-16 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panorama of new ideas in mathematics that are driving innovation in computing and communications.
Author : C.j. Goh
Publisher : Taylor & Francis
ISBN 13 : 9780415274791
Total Pages : 344 pages
Book Rating : 4.2/5 (747 download)
Download or read book Duality in Optimization and Variational Inequalities written by C.j. Goh and published by Taylor & Francis. This book was released on 2002-05-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.
Author : Aharon Ben-Tal
Publisher : SIAM
ISBN 13 : 0898714915
Total Pages : 500 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)
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.
Author : Hans Föllmer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110463458
Total Pages : 608 pages
Book Rating : 4.1/5 (14 download)
Download or read book Stochastic Finance written by Hans Föllmer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 1611976596
Total Pages : 540 pages
Book Rating : 4.6/5 (119 download)
Download or read book Lectures on Stochastic Programming: Modeling and Theory, Third Edition written by Alexander Shapiro and published by SIAM. This book was released on 2021-08-19 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and rigorous presentation of contemporary models and ideas of stochastic programming, this book focuses on optimization problems involving uncertain parameters for which stochastic models are available. Since these problems occur in vast, diverse areas of science and engineering, there is much interest in rigorous ways of formulating, analyzing, and solving them. This substantially revised edition presents a modern theory of stochastic programming, including expanded and detailed coverage of sample complexity, risk measures, and distributionally robust optimization. It adds two new chapters that provide readers with a solid understanding of emerging topics; updates Chapter 6 to now include a detailed discussion of the interchangeability principle for risk measures; and presents new material on formulation and numerical approaches to solving periodical multistage stochastic programs. Lectures on Stochastic Programming: Modeling and Theory, Third Edition is written for researchers and graduate students working on theory and applications of optimization, with the hope that it will encourage them to apply stochastic programming models and undertake further studies of this fascinating and rapidly developing area.
Author : David Yang Gao
Publisher : Springer
ISBN 13 : 3319580175
Total Pages : 374 pages
Book Rating : 4.3/5 (195 download)
Download or read book Canonical Duality Theory written by David Yang Gao and published by Springer. This book was released on 2017-10-09 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
