Author: Yves Achdou,Olivier Pironneau
Category: Options (Finance)
The authors review some important aspects of finance modeling involving partial differential equations and focus on numerical algorithms for the fast and accurate pricing of financial derivatives and for the calibration of parameters. This book explores the best numerical algorithms and discusses them in depth, from their mathematical analysis up to their implementation in C++ with efficient numerical libraries.
Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field
Bordeaux, June 2010
Author: René Carmona,Pierre Del Moral,Peng Hu,Nadia Oudjane
Publisher: Springer Science & Business Media
Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
Author: Curtis R. Vogel
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Stochastic Approximation Methods
Author: Dmitrii S. Silvestrov
Publisher: Walter de Gruyter
This book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. It is the first volume of the comprehensive two volumes monograph.
Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011
Author: Andrea Cangiani,Ruslan L Davidchack,Emmanuil H. Georgoulis,Alexander Gorban,Jeremy Levesley,Michael V. Tretyakov
Publisher: Springer Science & Business Media
The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
Author: Jorge J. More,Stephen J. Wright
Mathematics of Computing -- Numerical Analysis.
Advances in Computational Science: Lectures Presented at the International Conference on Computational Methods in Sciences and Engineering 2008
Author: George Maroulis,Theodore E. Simos
Publisher: American Inst. of Physics
The aim of ICCMSE 2008 is to bring together computational scientists and engineers from several disciplines in order to share methods, methodologies and ideas. The potential readers are all the scientists with interest in: Computational Mathematics, Theoretical Physics, Computational Physics, Theoretical Chemistry, Computational Chemistry, Mathematical Chemistry, Computational Engineering, Computational Mechanics, Computational Biology and Medicine, Scientific Computation, High Performance Computing, Parallel and Distributed Computing, Visualization, Problem Solving Environments, Software Tools, Advanced Numerical Algorithms, Modelling and Simulation of Complex Systems, Web-based Simulation and Computing, Grid-based Simulation and Computing, Computational Grids, and Computer Science.
Author: Yanfei Wang,Anatoly G. Yagola,Changchun Yang
Publisher: Walter de Gruyter
This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. Readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.
The Theory and Practice of Financial Engineering
Author: Paul Wilmott
Category: Business & Economics
Derivatives by Paul Wilmott provides the most comprehensive and accessible analysis of the art of science in financial modeling available. Wilmott explains and challenges many of the tried and tested models while at the same time offering the reader many new and previously unpublished ideas and techniques. Paul Wilmott has produced a compelling and essential new work in this field. The basics of the established theories-such as stochastic calculus, Black-Scholes, binomial trees and interest-rate models-are covered in clear and precise detail, but Derivatives goes much further. Complex models-such as path dependency, non-probabilistic models, static hedging and quasi-Monte Carlo methods-are introduced and explained to a highly sophisticated level. But theory in itself is not enough, an understanding of the role the techniques play in the daily world of finance is also examined through the use of spreadsheets, examples and the inclusion of Visual Basic programs. The book is divided into six parts: Part One: acts as an introduction and explanation of the fundamentals of derivatives theory and practice, dealing with the equity, commodity and currency worlds. Part Two: takes the mathematics of Part One to a more complex level, introducing the concept of path dependency. Part Three: concerns extensions of the Black-Scholes world, both classic and modern. Part Four: deals with models for fixed-income products. Part Five: describes models for risk management and measurement. Part Six: delivers the numerical methods required for implementing the models described in the rest of the book. Derivatives also includes a CD containing a wide variety of implementation material related to the book in the form of spreadsheets and executable programs together with resource material such as demonstration software and relevant contributed articles. At all times the style remains readable and compelling making Derivatives the essential book on every finance shelf.
Author: Stefan Banach International Mathematical Center
"This volume contains 15 papers contributed by the participands of the 2nd General AMaMeF conference and Banach Center converence 'Advances in mathematics of finance' organized in Bȩdlewo, Poland from 30th April till 5th May, 2007. AMaMeF (Advances Mathematical Methods of Finance) is a scientific programme of the European Science Foundation for 2005-2010"--Preface (p. 5).
Author: Charles Van Loan
The author captures the interplay between mathematics and the design of effective numerical algorithms.
Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations
Author: Changpin Li,Yujiang Wu,Ruisong Ye
Publisher: World Scientific
Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation. Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed. In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc. In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications. Contents:Gronwall Inequalities (Fanhai Zeng, Jianxiong Cao and Changpin Li)Existence and Uniqueness of the Solutions to the Fractional Differential Equations (Yutian Ma, Fengrong Zhang and Changpin Li)Finite Element Methods for Fractional Differential Equations (Changpin Li and Fanhai Zeng)Fractional Step Method for the Nonlinear Conservation Laws with Fractional Dissipation (Can Li and Weihua Deng)Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation (Tinggang Zhao and Haiyan Xuan)A Discontinuous Finite Element Method for a Type of Fractional Cauchy Problem (Yunying Zheng)Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain (Yu-Jiang Wu, Na Zhang and Lun-Ji Song)Incremental Unknowns Methods for the ADI and ADSI Schemes (Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang)Stability of a Collocated FV Scheme for the 3D Navier–Stokes Equations (Xu Li and Shu-qin Wang)Computing the Multiple Positive Solutions to p–Henon Equation on the Unit Square (Zhaoxiang Li and Zhonghua Yang)Multilevel WBIUs Methods for Reaction–Diffusion Equations (Yang Wang, Yu-Jiang Wu and Ai-Li Yang)Models and Dynamics of Deterministically Growing Networks (Weigang Sun, Jingyuan Zhang and Guanrong Chen)On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks (Yuan Chai and Li-Qun Chen)Chaotic Dynamical Systems on Fractals and Their Applications to Image Encryption (Ruisong Ye, Yuru Zou and Jian Lu)Planar Crystallographic Symmetric Tiling Patterns Generated From Invariant Maps (Ruisong Ye, Haiying Zhao and Yuanlin Ma)Complex Dynamics in a Simple Two-Dimensional Discrete System (Huiqing Huang and Ruisong Ye)Approximate Periodic Solutions of Damped Harmonic Oscillators with Delayed Feedback (Qian Guo)The Numerical Methods in Option Pricing Problem (Xiong Bo)Synchronization and Its Control Between Two Coupled Networks (Yongqing Wu and Minghai Lü) Readership: Senior undergraduates, postgraduates and experts in nonlinear dynamics with numerical analysis. Keywords:Fractional Dynamics;Infinite Dimensional Dynamics;Network Dynamics;Fractal DynamicsKey Features:The topics in this edited book are very hot and highly impressiveIssues and methods of such topics in this edited book have not been made available yetThe present edited book is suitable for various levels of researchers, such as senior undergraduates, postgraduates, and experts
Modeling, Analysis, and Control
Author: Jerry J. Batzel,Franz Kappel,Daniel Schneditz,Hien T. Tran
Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships. Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted. Researchers and graduate students in mathematical biology and biomedical engineering will find this book useful. It will also appeal to researchers in the physiological and life sciences who are interested in mathematical modeling.
Author: Giulia Di Nunno,Bernt Øksendal
Publisher: Springer Science & Business Media
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.
Author: Fabio Canova
Publisher: Princeton University Press
Category: Business & Economics
The last twenty years have witnessed tremendous advances in the mathematical, statistical, and computational tools available to applied macroeconomists. This rapidly evolving field has redefined how researchers test models and validate theories. Yet until now there has been no textbook that unites the latest methods and bridges the divide between theoretical and applied work. Fabio Canova brings together dynamic equilibrium theory, data analysis, and advanced econometric and computational methods to provide the first comprehensive set of techniques for use by academic economists as well as professional macroeconomists in banking and finance, industry, and government. This graduate-level textbook is for readers knowledgeable in modern macroeconomic theory, econometrics, and computational programming using RATS, MATLAB, or Gauss. Inevitably a modern treatment of such a complex topic requires a quantitative perspective, a solid dynamic theory background, and the development of empirical and numerical methods--which is where Canova's book differs from typical graduate textbooks in macroeconomics and econometrics. Rather than list a series of estimators and their properties, Canova starts from a class of DSGE models, finds an approximate linear representation for the decision rules, and describes methods needed to estimate their parameters, examining their fit to the data. The book is complete with numerous examples and exercises. Today's economic analysts need a strong foundation in both theory and application. Methods for Applied Macroeconomic Research offers the essential tools for the next generation of macroeconomists.
Mathematics, Stochastics and Computation
Author: Desmond Higham
Publisher: Cambridge University Press
This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.
Author: C. T. Kelley
Category: Iterative methods (Mathematics)
Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.