Quantum Field Theory for Economics and Finance

An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance.

Belal Ehsan Baaquie (Author)

9781108423151, Cambridge University Press

Hardback, published 23 August 2018

714 pages, 183 b/w illus. 21 tables
25.3 x 17.8 x 3.7 cm, 1.56 kg

'This book could be just the volume for someone wanting to make the transition from calculating matrix elements to designing financial instruments, from spinors to swaps or from operators to options … The book's structure interleaves traditional lessons in quantum field theory with topics in econophysics, producing a rather novel result.' Stephen J. Blundell, Contemporary Physics

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. ?-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.

Subject Areas: Statistical physics [PHS], Economic statistics [KCHS], Econometrics [KCH]