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Author: Andras Vanyolos Publisher: ISBN: Category : Languages : en Pages : 5
Book Description
Abstract In this paper we give a new derivation of the leading order term of the implied volatility in the SABR model. As is widely know, Hagan et al. obtained an analytic formula for the implied volatility via asymptotic expansion. It has been argued that the leading order term of this expansion contains an error and some authors have recalculated it using different methods. Here we give another derivation using standard perturbation theory of the underlying eikonal equation. Our result agrees with that found by Berestycki et al.
Author: Andras Vanyolos Publisher: ISBN: Category : Languages : en Pages : 5
Book Description
Abstract In this paper we give a new derivation of the leading order term of the implied volatility in the SABR model. As is widely know, Hagan et al. obtained an analytic formula for the implied volatility via asymptotic expansion. It has been argued that the leading order term of this expansion contains an error and some authors have recalculated it using different methods. Here we give another derivation using standard perturbation theory of the underlying eikonal equation. Our result agrees with that found by Berestycki et al.
Author: Peregrina Quintela Publisher: Springer ISBN: 3319630822 Category : Mathematics Languages : en Pages : 749
Book Description
This book addresses mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Using the classification system defined in the EU Framework Programme for Research and Innovation H2020, several of the topics covered belong to the challenge climate action, environment, resource efficiency and raw materials; and some to health, demographic change and wellbeing; while others belong to Europe in a changing world – inclusive, innovative and reflective societies. The 19th European Conference on Mathematics for Industry, ECMI2016, was held in Santiago de Compostela, Spain in June 2016. The proceedings of this conference include the plenary lectures, ECMI awards and special lectures, mini-symposia (including the description of each mini-symposium) and contributed talks. The ECMI conferences are organized by the European Consortium for Mathematics in Industry with the aim of promoting interaction between academy and industry, leading to innovation in both fields and providing unique opportunities to discuss the latest ideas, problems and methodologies, and contributing to the advancement of science and technology. They also encourage industrial sectors to propose challenging problems where mathematicians can provide insights and fresh perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.
Author: Victor Isakov Publisher: American Mathematical Soc. ISBN: 0821815326 Category : Mathematics Languages : en Pages : 209
Book Description
A careful exposition of a research field of current interest. This includes a brief survey of the subject and an introduction to recent developments and unsolved problems.
Author: Wolfgang Arendt Publisher: Springer Science & Business Media ISBN: 9783764371074 Category : Mathematics Languages : en Pages : 844
Book Description
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
Author: Alain Miranville Publisher: SIAM ISBN: 1611975921 Category : Mathematics Languages : en Pages : 216
Book Description
This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Author: Martin Braun Publisher: Springer Science & Business Media ISBN: 1461254272 Category : Mathematics Languages : en Pages : 390
Book Description
The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks.
Author: Nikos Mastorakis Publisher: Springer Science & Business Media ISBN: 0387764836 Category : Mathematics Languages : en Pages : 443
Book Description
Recent Advances in Numerical Methods features contributions from distinguished researchers, focused on significant aspects of current numerical methods and computational mathematics. The increasing necessity to present new computational methods that can solve complex scientific and engineering problems requires the preparation of this volume with actual new results and innovative methods that provide numerical solutions in effective computing times. Each chapter will present new and advanced methods and modern variations on known techniques that can solve difficult scientific problems efficiently.
Author: J. E. Dennis, Jr. Publisher: SIAM ISBN: 9781611971200 Category : Mathematics Languages : en Pages : 394
Book Description
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author: Andras Vanyolos
Author: Andras Vanyolos
Author: Peregrina Quintela
Author: 
Author: Alan L. Lewis
Author: Victor Isakov
Author: Wolfgang Arendt
Author: Alain Miranville
Author: Martin Braun
Author: Nikos Mastorakis
Author: J. E. Dennis, Jr.