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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
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.
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.
The 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. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011
Author: Andrea Cangiani
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.
Advances in Computational Science: Lectures Presented at the International Conference on Computational Methods in Sciences and Engineering 2008
Author: George Maroulis
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: 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).