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"Everything you need to know in order to manage risk effectively within your organizationYou cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive. This exciting branch of mathematics has very direct practical implications: when a new model is tested and implemented it can have an immediate impact on the financial environment.With risk management top of the agenda for many organizations, this book is essential reading for getting to grips with the mathematical story behind the subject of financial risk management. It will take you on a journey--from the early ideas of risk quantification up to today's sophisticated models and approaches to business risk management.To help you investigate the most up-to-date, pioneering developments in modern risk management, the book presents statistical theories and shows you how to put statistical tools into action to investigate areas such as the design of mathematical models for financial volatility or calculating the value at risk for an investment portfolio. Respected academic author Simon Hubbert is the youngest director of a financial engineering program in the U.K. He brings his industry experience to his practical approach to risk analysis Captures the essential mathematical tools needed to explore many common risk management problems Website with model simulations and source code enables you to put models of risk management into practice Plunges into the world of high-risk finance and examines the crucial relationship between the risk and the potential reward of holding a portfolio of risky financial assets This book is your one-stop-shop for effective risk management"-- "The book is self-contained and takes the reader on a mathematical journey from the early ideas of risk quantification up to the sophisticated models and approaches of the present day, linking and highlighting the milestones along the way"--

Risk management --- Capital market --- BUSINESS & ECONOMICS / Insurance / Risk Assessment & Management. --- Mathematical models. --- BUSINESS & ECONOMICS --- Insurance --- Risk Assessment & Management. --- Business & economics --- Risk assessment & management. --- Mathématiques --- Gestion du risque --- Mathématiques

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This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.

Mathematics. --- Approximations and Expansions. --- Partial Differential Equations. --- Numerical Analysis. --- Global Analysis and Analysis on Manifolds. --- Geophysics/Geodesy. --- Physical geography. --- Global analysis. --- Differential equations, partial. --- Numerical analysis. --- Mathématiques --- Géographie physique --- Analyse numérique --- Radial basis functions. --- Spherical functions. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Basis functions, Radial --- Functions, Radial basis --- Radial basis function method --- Functions, Spherical --- Geophysics. --- Approximation theory. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Approximation theory --- Spherical harmonics --- Transcendental functions --- Spheroidal functions --- Geography --- Mathematical analysis --- Partial differential equations --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Geometry, Differential --- Topology