Quantum Field Theory for Economics and Finance
Cambridge University Press, 8/23/2018
EAN 9781108423151, ISBN10: 1108423159
Hardcover, 714 pages, 25.3 x 17.8 x 3.7 cm
Language: English
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.
Foreword
Preface
Acknowledgements
1. Synopsis
Part I. Introduction
2. Quantum mechanics
3. Classical field theory
4. Acceleration action
5. Option theory
6. Path integral of asset prices
Part II. Linear Quantum Fields
7. Scalar quantum field
8. Dirac spinor field
9. Photon gauge field
10. Forward interest rates' quantum field
11. Risky interest rates' quantum fields
12. Bonds
index-linked stochastic coupons
Part III. Nonlinear Quantum Fields
13. Operator expectation and S matrix
14. Nonlinear scalar field
Feynman diagrams
15. Renormalization
16. β-function
fixed points
17. Renormalization group and phase transitions
18. Effective action
19. Nonlinear interest rates' quantum field
20. Simulation of nonlinear interest rates
21. Interest rates range accrual swap
Part IV. 2D Quantum Fields
22. Two dimensional quantum electrodynamics
23. Bosonic string theory
24. Futures asset prices
25. Epilogue
References
Index.