Mathematical Methods and Quantum Mathematics for Economics and Finance

Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and financeand leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economicsand finance. In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton's theory of corporate debt are among topics analyzed using quantum mathematics.

Provides a concise and up-to-date introduction for all graduate students studying finance/quantitative finance Includes a wealth of examples and exercises to promote student comprehension Discusses the Black-Scholes equation to help students understand the mathematical underpinning of financial instruments

Autorentext

Prof. Belal Ehsan Baaquie holds a B.S. in Physics from Caltech and a Ph.D. in Theoretical Physics from Cornell University, USA. His main research interest is in the study and application of mathematical methods from quantum field theory. He has applied the mathematical formalism of field theory to finance and been a major contributor to the emerging field of quantum finance. His current focus is on developing the formalism of quantum finance and applying it to option pricing, corporate coupon bonds, and the theory of interest rates, as well as the study of equity, foreign exchange, and commodities. He is also applying methodologies from statistical mechanics and quantum field theory to the study of microeconomics and macroeconomics.

Inhalt
Acknowledgements.- Preface.- PART I : Introduction.- PART II : Linear Algebra.- PART III : Calculus.- PART IV : Probability Theory.- PART V: Quantum Mathematics.- Bibliography.- Index