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Mathematical methods for finance : tools for asset and risk management
The mathematical and statistical tools needed in the rapidly growing quantitative finance field
With the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, part of the Frank J. Fabozzi Series, has been created with this in mind. Designed to provide the tools needed to apply finance theory to real world financial markets, this book offers a wealth of insights and guidance in practical applications.
It contains applications that are broader in scope from what is covered in a typical book on mathematical techniques. Most books focus almost exclusively on derivatives pricing, the applications in this book cover not only derivatives and asset pricing but also risk management—including credit risk management—and portfolio management.
* Includes an overview of the essential math and statistical skills required to succeed in quantitative finance
* Offers the basic mathematical concepts that apply to the field of quantitative finance, from sets and distances to functions and variables
* The book also includes information on calculus, matrix algebra, differential equations, stochastic integrals, and much more
* Written by Sergio Focardi, one of the world's leading authors in high-level finance
Drawing on the author's perspectives as a practitioner and academic, each chapter of this book offers a solid foundation in the mathematical tools and techniques need to succeed in today's dynamic world of finance.
eBook
Monte Carlo Simulation with Applications to Finance
Developed from the author's course on Monte Carlo simulation at Brown University, this text provides a self-contained introduction to Monte Carlo methods in financial engineering. It covers common variance reduction techniques, the cross-entropy method, and the simulation of diffusion process models. Requiring minimal background in mathematics and finance, the book includes numerous examples of option pricing, risk analysis, and sensitivity analysis as well as many hand-and-paper and MATLAB coding exercises at the end of every chapter.
eBook
The handbook of post crisis financial modelling
The 2008 financial crisis was a watershed moment which clearly influenced the public's perception of the role of 'finance' in society. This is the first comprehensive handbook to look at financial modelling post crisis from the legal/historical; empirical modelling; stochastic; and non-stochastic modelling perspectives.
eBook
Mathematics and statistics for financial risk management
\"This is an excellent book to grasp the basics of financial risk management. Everything in the book is explained from scratch and the concepts are very well exemplified with real life situations. Accompanied with a website filled with excel sheets for application, the book is great for future course material. This Second Edition of Mathematics and Statistics for Financial Risk Management includes 2 new chapters. The first chapter is on Bayesian Analysis and covers Bayes' Theorem, Many State Problems, Continuous Distributions, Bayesian Networks, and Bayesian Networks versus Correlation Matrices. The second new chapter is on Hypothesis Testing & Confidence Intervals and is on The Sample Mean Revisited, Sample Variance Revisited, Confidence Intervals, Hypothesis Testing, Chebyshev's Inequality, and Application: VaR. All chapters will have problems for testing and answers online\"-- Provided by publisher.
Book
Game-theoretic foundations for probability and finance
Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk's Probability and Finance , published in 2001, showed that perfect-information games can be used to define mathematical probability.
eBook
Monte Carlo simulation with applications to finance
\"Preface This book can serve as the text for a one-semester course on Monte Carlo simulation. The intended audience is advanced undergraduate students or students on master's programs who wish to learn the basics of this exciting topic and its applications to finance. The book is largely self-contained. The only prerequisite is some experience with probability and statistics. Prior knowledge on option pricing is helpful but not essential. As in any study of Monte Carlo simulation, coding is an integral part and cannot be ignored. The book contains a large number of MATLAB coding exercises. They are designed in a progressive manner so that no prior experience with MATLAB is required. Much of the mathematics in the book is informal. For example, randomvariables are simply defined to be functions on the sample space, even though they should be measurable with respect to appropriate algebras; exchanging the order of integrations is carried out liberally, even though it should be justified by the Tonelli-Fubini Theorem. The motivation for doing so is to avoid the technical measure theoretic jargon, which is of little concern in practice and does not help much to further the understanding of the topic. The book is an extension of the lecture notes that I have developed for an undergraduate course on Monte Carlo simulation at Brown University. I would like to thank the students who have taken the course, as well as the Division of Applied Mathematics at Brown, for their support. Hui Wang Providence, Rhode Island January, 2012\"-- Provided by publisher.
Book
On time-inconsistent stochastic control in continuous time
In this paper, which is a continuation of the discrete-time paper (Björk and Murgoci in Finance Stoch. 18:545–592,
2004
), we study a class of continuous-time stochastic control problems which, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We study these problems within a game-theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled continuous-time Markov process and a fairly general objective functional, we derive an extension of the standard Hamilton–Jacobi–Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy as well as the equilibrium value function. The main theoretical result is a verification theorem. As an application of the general theory, we study a time-inconsistent linear-quadratic regulator. We also present a study of time-inconsistency within the framework of a general equilibrium production economy of Cox–Ingersoll–Ross type (Cox et al. in Econometrica 53:363–384,
1985
).
Journal Article