Book Description
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 highlevel 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.
Table of Contents
 Cover
 Series Page
 Title Page
 Copyright Page
 Dedication
 Preface
 About the Authors
 Chapter 1: Basic Concepts
 Chapter 2: Differential Calculus
 Chapter 3: Integral Calculus
 Chapter 4: Matrix Algebra

Chapter 5: Probability
 INTRODUCTION
 REPRESENTING UNCERTAINTY WITH MATHEMATICS
 PROBABILITY IN A NUTSHELL
 OUTCOMES AND EVENTS
 PROBABILITY
 MEASURE
 RANDOM VARIABLES
 INTEGRALS
 DISTRIBUTIONS AND DISTRIBUTION FUNCTIONS
 RANDOM VECTORS
 STOCHASTIC PROCESSES
 PROBABILISTIC REPRESENTATION OF FINANCIAL MARKETS
 INFORMATION STRUCTURES
 FILTRATION
 KEY POINTS

Chapter 6: Probability
 INTRODUCTION
 CONDITIONAL PROBABILITY AND CONDITIONAL EXPECTATION
 MOMENTS AND CORRELATION
 COPULA FUNCTIONS
 SEQUENCES OF RANDOM VARIABLES
 INDEPENDENT AND IDENTICALLY DISTRIBUTED SEQUENCES
 SUM OF VARIABLES
 GAUSSIAN VARIABLES
 APPPROXIMATING THE TAILS OF A PROBABILITY DISTRIBUTION: CORNISHFISHER EXPANSION AND HERMITE POLYNOMIALS
 THE REGRESSION FUNCTION
 FAT TAILS AND STABLE LAWS
 KEY POINTS
 Chapter 7: Optimization
 Chapter 8: Difference Equations

Chapter 9: Differential Equations
 INTRODUCTION
 DIFFERENTIAL EQUATIONS DEFINED
 ORDINARY DIFFERENTIAL EQUATIONS
 SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
 CLOSEDFORM SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
 NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
 NONLINEAR DYNAMICS AND CHAOS
 PARTIAL DIFFERENTIAL EQUATIONS
 KEY POINTS
 Chapter 10: Stochastic Integrals
 Chapter 11: Stochastic Differential Equations
 Index
Product Information
 Title: Mathematical Methods for Finance: Tools for Asset and Risk Management
 Author(s):
 Release date: September 2013
 Publisher(s): Wiley
 ISBN: 9781118421499