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 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.
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: CORNISH-FISHER 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
- CLOSED-FORM 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: 9781118312636
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