Tuesday, October 1, 2019

The Mathematics of Financial Modeling and Investment Management

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This book is designed to be a working tool for the investment management practitioner, student, and researcher. We cover the process of financial decision-making and its economic foundations. We present financial models and theories, including CAPM, APT, factor models, models of the term structure of interest rates, and optimization methodologies. Special emphasis is put on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. For example, tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are recent advances in financial economics that we discuss in depth.

Special emphasis has been put on describing concepts and mathematical techniques, leaving aside lengthy demonstrations, which, while the substance of mathematics, are of limited interest to the practitioner and student of financial economics. From the practitioner’s point of view, what is important is to have a firm grasp of the concepts and techniques, which will allow one to interpret the results of simulations and analyses that are now an integral part of finance.

There is no prerequisite mathematical knowledge for reading this book: all mathematical concepts used in the book are explained, starting from ordinary calculus and matrix algebra. It is, however, a demanding book given the breadth and depth of concepts covered. Mathematical concepts are in bolded type when they appear for the first time in the book, economic and finance concepts are italicized when they appear for the first time.

About the Authors
Commonly Used Symbols
Abbreviations and Acronyms
CHAPTER 1: From Art to Engineering in Finance
CHAPTER 2: Overview of Financial Markets, Financial Assets, and Market Participants
CHAPTER 3: Milestones in Financial Modeling and Investment Management
CHAPTER 4: Principles of Calculus
CHAPTER 5: Matrix Algebra
CHAPTER 6: Concepts of Probability
CHAPTER 7: Optimization
CHAPTER 8: Stochastic Integrals
CHAPTER 9: Differential Equations and Difference Equations
CHAPTER 10: Stochastic Differential Equations
CHAPTER 11: Financial Econometrics: Time Series Concepts, Representations, and Models
CHAPTER 12: Financial Econometrics: Model Selection, Estimation, and Testing
CHAPTER 13: Fat Tails, Scaling, and Stable Laws
CHAPTER 14: Arbitrage Pricing: Finite-State Models
CHAPTER 15: Arbitrage Pricing: Continuous-State, Continuous-Time Models
CHAPTER 16: Portfolio Selection Using Mean-Variance Analysis
CHAPTER 17: Capital Asset Pricing Model
CHAPTER 18: Multifactor Models and Common Trends for Common Stocks
CHAPTER 19: Equity Portfolio Management
CHAPTER 20: Term Structure Modeling and Valuation of Bonds and Bond Options
CHAPTER 21: Bond Portfolio Management
CHAPTER 22: Credit Risk Modeling and Credit Default Swaps
CHAPTER 23: Risk Management

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