Breton, Michele; Ben-Ameur, Hatem (Eds.)

Numerical Methods in Finance

2005, X, 258 p., Hardcover
ISBN: 0-387-25117-0

About this book

The use of mathematical models and numerical techniques in finance is a growing practice, and an increasing number of applied mathematicians are working on applications in finance and business. Numerical Methods in Finance presents some exciting developments arising from the combination of mathematics, numerical analysis, and finance. It covers a wide range of topics, from portfolio management and asset pricing, to performance, risk, debt and real option evaluation. It also presents applications of a variety of cutting edge approaches and techniques, including robust control, min-max optimisation, Bessel processes, stochastic viability, variational inequalities, and Monte-Carlo test techniques. Numerical Methods in Finance also presents surveys of models and approaches in specific areas in finance, such as corporate debt valuation and portfolio selection.

Table of contents

Foreword. Avant-propos. Contributing Authors. Preface.
1. Corporate Debt Valuation: The Structural Approach, P. Francois
2. Bessel Processes and Asian Options, D. Dufresne
3. Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty, J.-P. Aubin, D. Pujal, and P. Saint-Pierre
4. The Robust Control Approach to Option Pricing and Interval Models: An Overview, P. Bernhard
5. A Finite Element Method for Two Factor Convertible Bonds, J. de Frutos
6. On Numerical Methods and the Valuation of American Options, M. Bellalah
7. Valuing American Contingent Claims when Time to Maturity is Uncertain, T. Berrada
8. Foreign Direct Investment: The Incentive to Expropriate and the Cost of Expropriation Risk, E. Clark
9. Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions, M.-C. Beaulieu, J.-M. Dufour, and L. Khalaf
10.A Stochastic Discount Factor-Based Approach for Fixed-income Mutual Fund Performance Evaluation, M.A. Ayadi and L. Kryzanowski
11.Portfolio Selection with Skewness, P. Boyle and B. Ding
12.Continuous Min-Max Approach for Single Period Portfolio Selection Problem, N. Gulpinar and B. Rustem

Warnecke, Gerald (Ed.)

Analysis and Numerics for Conservation Laws

2005, VII, 542 p. HardcoverISBN: 3-540-24834-X

About this book

The priority research program Analysis and Numerics for Conservation Laws was funded by the German research foundation Deutsche Forschungsgemeinschaft (DFG) for a period of six years starting in 1997. The diversity of topics, represented in the present book, was one of the strengths of the research program. Research groups of very different background, most of which were interacting for the first time, contributed to this interdisciplinary work.

The present book contains contributions from interlinked participating projects ranging from the analysis of hyperbolic systems of first order partial differential equations, the development of improved numerical methods for these equations to applications in astrophysics and engineering. It aims at conveying their results achieved in the program to readers outside of their own particular field.

The book contains a large number of figures and a number of color plates. The reader can find an up-to-date presentation of many current research topics in the field.

Table of contents

S.Andreae, J.Ballmann, S.Muller: Wave Processes at Interfaces.- J.Heiermann, M.Auweter-Kurtz, Ch.Sleziona: Numerics for Magnetoplasmadynamic Propulsion.- H.Babovsky: Hexagonal Kinetic Models and the Numerical Simulation of Kinetic Boundary Layers.- R.Deiterding, G.Bader: High-resolution Simulation of Detonations with Detailed Chemistry.- A.S.Bormann: Numerical Linear Stability Analysis for Compressible Fluids.- M.Schussler, J.H.M.J.Bruls, A.Vogler, P. Vollmoller: Simulation of Solar Radiative Magneto-Convection.- W.Dahmen, S.Muller, A.Vos: Riemann Problem for the Euler Equation with Non-Convex Equation of State Including Phase Transitions.- A.Dedner, D.Kroner, C.Rohde, M.Wesenberg: Radiation Magnetohydrodynamics: Analysis for Model Problems and Efficient 3d-Simulations for the Full System.- W.Dreyer, M.Herrmann, M.Kunik, S.Qamar: Kinetic Schemes for Selected Initial and Boundary Value Problems.- F.Volker, R.Vilsmeier, D.Hanel: A Local Level-Set Method under Involvement of Topological Aspects.- T.Hillen, K.P.Hadeler: Hyperbolic Systems and Transport Equations in Mathematical Biology.- J.Harterich, St. Liebscher: Travelling Waves in Systems of Hyperbolic Balance Laws.- R.Hartmann: The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations.- Ch.Helling, R.Klein, E.Sedlmayr: The Multi-Scale Dust Formation in Substellar Atmospheres.- D.Hietel, M.Junk, J. Kuhnert, S.Tiwari: Meshless Methods for Conservation Laws.- W.Hillbrandt, M.Reinecke, W.Schmidt, F.K.Ropke, C.Travaglio, J.C.Niemeyer: Simulations of Turbulent Thermonuclear Burining in Type 1a Supernovae.- Y.L.Lee, R.Schneider, C.-D.Munz, F.Kemm: Hyperbolic GLM Scheme for Elliptic Constraints in Computational Electromagnetics and MHD.- H.Schmidt, R.Klein: Flexible Flame Structure Modelling in a Flame Front Tracking Scheme.- T.Kroger, S.Noelle: Riemann-Solver Free Schemes.- H.Liu: Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes.- S.Noelle, W.Rosenbaum, M.Rumpf: Multidimensional Adaptive Staggered Grids.- W.-A.Yong, W.Jager: On Hyperbolic Relaxation Problems.- Appendix: Color Plates.

Sixten Lundstrom, Carl-Erik Sarndal

Estimation in Surveys with Nonresponse

ISBN: 0-470-01133-5
Hardcover 212 pages August 2005

There is increasing interest in the study of nonresponse in statistical surveys, as there is a need to reduce the level of nonresponse in order to increase the validity of the results, and to deal with the problem of nonresponse once it has arisen. It is possible to reduce the amount of nonresponse in a survey, but not possible to avoid it completely. Therefore there is a need for techniques that enable the survey statistician to estimate the level of nonresponse, and adjust for it accordingly in order to improve the results. This book presents a practical overview of techniques for estimating nonresponse in statistical surveys, and for adjusting for it once it has occurred. It also covers the related topics of frame imperfections and coverage errors in surveys, featuring many worked examples and implementation of the methods in a number of statistical software packages. The text is based upon a manual developed at Statistics Sweden, and used extensively by government statisticians working with data from real surveys.
Features:

Provides an overview of methods for the estimation of nonresponse in statistical surveys.
Covers a range of methods for nonresponse adjustment, particularly reweighting and imputation.
Includes guidelines for dealing with frame imperfections and coverage errors.
Features worked examples throughout using real data.
Includes implementation of the methods in a range of statistical software
It will appeal to researchers and practitioners analyzing data from statistical surveys. Also suitable as supplementary reading for graduate students of survey statistics.

Ahmed A. Shabana
University of Illinois, Chicago

Dynamics of Multibody Systems, 3rd Edition

Hardback (ISBN: 0-521-85011-8)

Published 2005 | 384 pages | 253 x 177 mm

Dynamics of Multibody Systems introduces multibody dynamics, with an emphasis on flexible body dynamics. Many common mechanisms such as automobiles, space structures, robots, and micro machines have mechanical and structural systems that consist of interconnected rigid and deformable components. The dynamics of these large-scale, multibody systems are highly nonlinear, presenting complex problems that in most cases can only be solved with computer-based techniques. The book begins with a review of the basic ideas of kinematics and the dynamics of rigid and deformable bodies before moving on to more advanced topics and computer implementation. This new edition includes important new developments relating to the problem of large deformations and numerical algorithms as applied to flexible multibody systems. The book’s wealth of examples and practical applications will be useful to graduate students, researchers, and practicing engineers working on a wide variety of flexible multibody systems.

Contents

1. Introduction; 2. Reference kinematics; 3. Analytical techniques; 4. Mechanics of deformable bodies; 5. Floating frame of reference formulation; 6. Finite element formulation; 7. Large deformation problem; Appendix: Linear algebra; References; Index.

Details
92 line diagrams 133 exercises
Weight: 0.835 kg

Edited by Bridget Webb

Surveys in Combinatorics 2005

Series: London Mathematical Society Lecture Note Series
Paperback (ISBN: 0-521-61523-2)
Not yet published - available from July 2005

This volume contains survey articles based on the invited lectures given at the Twentieth British Combinatorial Conference, organized jointly by the University of Durham and the Open University. It was held in July 2005 at the University of Durham. This biennial conference is a well-established international event, with speakers from all over the world. By its nature this volume provides an up-to-date overview of current research activity in several areas of combinatorics, ranging from combinatorial number theory to geometry. The authors are some of the world's foremost researchers in their fields.

Contents

1. Finite field models in additive combinatorics Ben Green; 2. The subgroup structure of finite classical groups in terms of geometric configurations Oliver H. King; 3. Constructing combinatorial objects via cliques Patric R. J. Ostergard; 4. Flocks of circle planes Tim Penttila; 5. Judicious partitions and related problems Alex Scott; 6. An isoperimetric method for the small sumset problem O. Serra; 7. The structure of claw-free graphs Maria Chudnovsky and Paul Seymour; 8. The multivariate Tutte polynomial (alias Potts model) for graphs and matroids Alan D. Sokal; 9. The sparse regularity lemma and its applications Stefanie Gerke and Angelika Steger.

Contributors

Ben Green, Oliver H. King, Patric R. J. Ostergard, Tim Penttila, Alex Scott, O. Serra, Maria Chudnovsky, Paul Seymour, Alan D. Sokal, Stefanie Gerke, Angelika Steger

Details
75 exercises
Weight: 0.39 kg

Keith Burns Northwestern University, Evanston, Illinois, USA
Marian Gidea Northeastern Illinois University, Chicago, USA

Differential Geometry and Topology: With a View to Dynamical Systems

Series: Studies in Advanced Mathematics Volume: 45

ISBN: 1584882530
Number of Pages: 400

Provides a clear introduction to three related subjects whose interplay enhances intuitive understanding
Focuses on geodesics as a tool for better understanding Riemannian geometry
Takes an example-based approach to the more cryptic notions of differential geometry, such as affine connection, covariant derivatives and curvature tensors
Incorporates a presentation of smooth dynamical systems on manifolds and hyperbolic systems

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow.

Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models.

The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow.

The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.

Table of Contents

MANIFOLDS
VECTOR FIELDS AND DYNAMICAL SYSTEMS
RIEMANNIAN METRICS
RIEMANNIAN CONNECTIONS AND GEODESICS
CURVATURE
TENSORS AND DIFFERENTIAL FORMS
FIXED POINTS AND INTERSECTION NUMBERS
MORSE THEORY
HYPERBOLIC SYSTEMS
References
Index