| Description |
1 online resource (xxvi, 690 pages) : illustrations |
| Summary |
An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum field theory. |
| Bibliography |
Includes bibliographical references (pages 680-685) and index. |
| Contents |
Cover; Half-title; Title page; Copyright information; Dedication; Table of contents; Foreword; Preface; Acknowledgments; 1 Synopsis; 1.1 Organization of the book; 1.2 What is a quantum field?; Part I Introduction; 2 Quantum mechanics; 2.1 Introduction; 2.2 Quantum principles; 2.3 Theory of measurement; 2.4 Dirac delta function; 2.5 Schrödinger and Heisenberg formalism; 2.6 Feynman path integral; 2.7 Hamiltonian and path integral; 2.8 Hamiltonian from Lagrangian; 2.9 Summary; 2.10 Appendix: Dirac bracket and vector notation; 2.11 Appendix: Gaussian integration; 2.11.1 Quadratic action |
|
2.11.2 Gaussian white noise3 Classical field theory; 3.1 Introduction; 3.2 Lagrangian mechanics; 3.3 Classical field equation; 3.4 Free scalar field; 3.5 Symmetries; 3.6 Noether's theorem; 3.7 Stress tensor; 3.7.1 Klein-Gordon field; 3.7.2 Electromagnetic field; 3.8 Spontaneous symmetry breaking; 3.9 Landau-Ginzburg Lagrangian; 3.9.1 Meissner effect; 3.10 Higgs mechanism; 3.11 Lorentz group; 3.12 Relativistic fields; 3.12.1 Scalar and vector fields; 3.12.2 Spinor fields; 3.13 Summary; 4 Acceleration action; 4.1 Action and Hamiltonian; 4.2 Transition amplitude: Hamiltonian |
|
5.10 Option price: Baaquie-Yang (BY) model5.11 Martingale: Conditional probability; 5.12 Market time; 5.13 Empirical results; 5.13.1 Equity options; 5.13.2 FX options; 5.14 FX options and market instability; 5.14.1 Euro; 5.14.2 Swiss franc; 5.15 Summary; 6 Path integral of asset prices*; 6.1 Introduction; 6.2 Microeconomic potential; 6.3 Microeconomic action functional; 6.4 Equilibrium asset prices; 6.4.1 Expansion of potential; 6.5 Feynman perturbation expansion; 6.5.1 Auto-correlation; 6.5.2 Cross-correlation; 6.5.3 Cubic and quartic terms; 6.6 Nonlinear terms: Feynman diagrams |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Economics -- Mathematical models.
|
|
Finance -- Mathematical models.
|
|
Quantum field theory.
|
|
BUSINESS & ECONOMICS -- Economics -- General. |
|
BUSINESS & ECONOMICS -- Reference. |
|
Modelos matemáticos |
|
Economics -- Mathematical models |
|
Finance -- Mathematical models |
|
Quantum field theory |
| Other Form: |
Print version: Baaquie, B.E. Quantum field theory for economics and finance. Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2018 9781108423151 (DLC) 2017061436 (OCoLC)1019845443 |
| ISBN |
9781108399685 (electronic bk.) |
|
1108399681 (electronic bk.) |
|
9781108503747 (electronic bk.) |
|
1108503748 (electronic bk.) |
|
9781108423151 (hardback) |
|
1108423159 (hardback) |
|
1108502423 |
|
9781108502429 |
|
