Abstract
Feynman’s method of path integration offers an alternative to the conventional solutions to the Schrodinger’s equation. Path integrals provide not only a new computational approach to quantum mechanics, but also a different conceptual perspective of view. The advantage of path integral manifests itself particularly when the number of particles (or number of degrees of freedom) of the many-body system increases. Furthermore, the formalism derived for the dynamics of a system can, after slight modification, be applied to calculate interesting quantities of systems in thermodynamic equilibrium.
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References
Feynman’s path integral method was best introduced in the following treatises, R.P. Feynman and A.R. Hibbs, “Quantum Mechanics and Path Integrals”, McGraw-Hill, New York (1965)
L.S. Schulman, “Techniques and Applications of Path Integration”, John Wiley & Sons, Inc., New York (1981)
The Black-Scholes equation was presented in, F. Black and M. J. Scholes, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, 81 (1973) 637–659
A more general path-integral formula for options pricing with variable volatility was derived in, B.E. Baaquie, “A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results”, J. de Phys. I (France), 7 (1997) 1733–1753, available at xxx.lanl.gov/cond-mat/9708178 22 Aug 1997
A path integral Monte Carlo evaluation of options prices can be found in, M.S. Makivic, “Numerical Pricing of Derivative Claims: Path Integral Monte Carlo Approach”, NPAC Technical Report SCCS 650, Syracuse University, 1994
Metropolis-Hastings algorithm was shown in, W.K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications”, Biometrika, 57 (1970) 97–109
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Wang, SC. (2003). Path Integral. In: Interdisciplinary Computing in Java Programming. The Springer International Series in Engineering and Computer Science, vol 743. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0377-4_10
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DOI: https://doi.org/10.1007/978-1-4615-0377-4_10
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