Some Formulas For The Conjugate Of Convex Risk Measures

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Lectures on Stochastic Programming: Modeling and Theory, Third Edition

Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 1611976596
Total Pages : 540 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Lectures on Stochastic Programming: Modeling and Theory, Third Edition by : Alexander Shapiro

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.

Lectures on Stochastic Programming

Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 1611973430
Total Pages : 512 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Lectures on Stochastic Programming by : Alexander Shapiro

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.

Handbook of the Fundamentals of Financial Decision Making

Author : Leonard C. MacLean
Publisher : World Scientific
ISBN 13 : 9814417351
Total Pages : 941 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Handbook of the Fundamentals of Financial Decision Making by : Leonard C. MacLean

Download or read book Handbook of the Fundamentals of Financial Decision Making written by Leonard C. MacLean and published by World Scientific. This book was released on 2013 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook in two parts covers key topics of the theory of financial decision making. Some of the papers discuss real applications or case studies as well. There are a number of new papers that have never been published before especially in Part II.Part I is concerned with Decision Making Under Uncertainty. This includes subsections on Arbitrage, Utility Theory, Risk Aversion and Static Portfolio Theory, and Stochastic Dominance. Part II is concerned with Dynamic Modeling that is the transition for static decision making to multiperiod decision making. The analysis starts with Risk Measures and then discusses Dynamic Portfolio Theory, Tactical Asset Allocation and Asset-Liability Management Using Utility and Goal Based Consumption-Investment Decision Models.A comprehensive set of problems both computational and review and mind expanding with many unsolved problems are in an accompanying problems book. The handbook plus the book of problems form a very strong set of materials for PhD and Masters courses both as the main or as supplementary text in finance theory, financial decision making and portfolio theory. For researchers, it is a valuable resource being an up to date treatment of topics in the classic books on these topics by Johnathan Ingersoll in 1988, and William Ziemba and Raymond Vickson in 1975 (updated 2 nd edition published in 2006).

A Cookbook with Probability One

Author : Damiano Rossello
Publisher : Springer Nature
ISBN 13 : 3031546881
Total Pages : 401 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis A Cookbook with Probability One by : Damiano Rossello

Download or read book A Cookbook with Probability One written by Damiano Rossello and published by Springer Nature. This book was released on with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Risk-Averse Optimization and Control

Author : Darinka Dentcheva
Publisher : Springer Nature
ISBN 13 : 3031579887
Total Pages : 462 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Risk-Averse Optimization and Control by : Darinka Dentcheva

Download or read book Risk-Averse Optimization and Control written by Darinka Dentcheva and published by Springer Nature. This book was released on with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convex Optimization

Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)

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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.

Handbook of Quantitative Finance and Risk Management

Author : Cheng-Few Lee
Publisher : Springer Science & Business Media
ISBN 13 : 0387771174
Total Pages : 1700 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Handbook of Quantitative Finance and Risk Management by : Cheng-Few Lee

Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.

Finance at Fields

Author : Matheus R. Grasselli
Publisher : World Scientific
ISBN 13 : 9814407887
Total Pages : 598 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Finance at Fields by : Matheus R. Grasselli

Download or read book Finance at Fields written by Matheus R. Grasselli and published by World Scientific. This book was released on 2013 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume in very broad, including papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the articles contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.

Unilateral Variational Analysis In Banach Spaces (In 2 Parts)

Author : Lionel Thibault
Publisher : World Scientific
ISBN 13 : 981125818X
Total Pages : 1629 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Unilateral Variational Analysis In Banach Spaces (In 2 Parts) by : Lionel Thibault

Download or read book Unilateral Variational Analysis In Banach Spaces (In 2 Parts) written by Lionel Thibault and published by World Scientific. This book was released on 2023-02-14 with total page 1629 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems.The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments.Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.

Mathematical Methods in Risk Theory

Author : Hans Bühlmann
Publisher : Springer Science & Business Media
ISBN 13 : 3540307117
Total Pages : 218 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Mathematical Methods in Risk Theory by : Hans Bühlmann

Download or read book Mathematical Methods in Risk Theory written by Hans Bühlmann and published by Springer Science & Business Media. This book was released on 2007-06-15 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time. The result is a systematic and very readable book, which takes into account the most recent developments of the field. It will be of great interest to the actuary as well as to the statistician . . ." -- Math. Reviews Vol. 43

Indifference Pricing

Author : René Carmona
Publisher : Princeton University Press
ISBN 13 : 0691138834
Total Pages : 427 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Indifference Pricing by : René Carmona

Download or read book Indifference Pricing written by René Carmona and published by Princeton University Press. This book was released on 2009-01-18 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets. René Carmona brings together a who's who of leading experts in the field to provide the definitive introduction for students, scholars, and researchers. Until recently, financial mathematicians and engineers developed pricing and hedging procedures that assumed complete markets. But markets are generally incomplete, and it may be impossible to hedge against all sources of randomness. Indifference Pricing offers cutting-edge procedures developed under more realistic market assumptions. The book begins by introducing the concept of indifference pricing in the simplest possible models of discrete time and finite state spaces where duality theory can be exploited readily. It moves into a more technical discussion of utility indifference pricing for diffusion models, and then addresses problems of optimal design of derivatives by extending the indifference pricing paradigm beyond the realm of utility functions into the realm of dynamic risk measures. Focus then turns to the applications, including portfolio optimization, the pricing of defaultable securities, and weather and commodity derivatives. The book features original mathematical results and an extensive bibliography and indexes. In addition to the editor, the contributors are Pauline Barrieu, Tomasz R. Bielecki, Nicole El Karoui, Robert J. Elliott, Said Hamadène, Vicky Henderson, David Hobson, Aytac Ilhan, Monique Jeanblanc, Mattias Jonsson, Anis Matoussi, Marek Musiela, Ronnie Sircar, John van der Hoek, and Thaleia Zariphopoulou. The first book on utility indifference pricing Explains the fundamentals of indifference pricing, from simple models to the most technical ones Goes beyond utility functions to analyze optimal risk transfer and the theory of dynamic risk measures Covers non-Markovian and partially observed models and applications to portfolio optimization, defaultable securities, static and quadratic hedging, weather derivatives, and commodities Includes extensive bibliography and indexes Provides essential reading for PhD students, researchers, and professionals

Computational and Analytical Mathematics

Author : David H. Bailey
Publisher : Springer Science & Business Media
ISBN 13 : 1461476216
Total Pages : 710 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Computational and Analytical Mathematics by : David H. Bailey

Download or read book Computational and Analytical Mathematics written by David H. Bailey and published by Springer Science & Business Media. This book was released on 2013-09-15 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop on ‘Computational and Analytical Mathematics’ held in May 2011 in celebration of Dr. Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches.

Mathematical Risk Analysis

Author : Ludger Rüschendorf
Publisher : Springer Science & Business Media
ISBN 13 : 364233590X
Total Pages : 414 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Mathematical Risk Analysis by : Ludger Rüschendorf

Download or read book Mathematical Risk Analysis written by Ludger Rüschendorf and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.

Conjugate Duality and Optimization

Author : R. Tyrrell Rockafellar
Publisher : SIAM
ISBN 13 : 9781611970524
Total Pages : 80 pages
Book Rating : 4.9/5 (75 download)

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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.

Stochastic Finance

Author : Hans Föllmer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110463458
Total Pages : 608 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Stochastic Finance by : Hans Föllmer

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

Convex Duality and Financial Mathematics

Author : Peter Carr
Publisher : Springer
ISBN 13 : 3319924923
Total Pages : 162 pages
Book Rating : 4.3/5 (199 download)

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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

Stochastics of Environmental and Financial Economics

Author : Fred Espen Benth
Publisher : Springer
ISBN 13 : 3319234250
Total Pages : 362 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Stochastics of Environmental and Financial Economics by : Fred Espen Benth

Download or read book Stochastics of Environmental and Financial Economics written by Fred Espen Benth and published by Springer. This book was released on 2015-10-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.