On the Application of Fokker-Planck Equation to Psychological Future Time
Author(s)
Ognjen Vukovic
Affiliation(s)
Department for Finance (MSc Student), University of Liechtenstein, Vaduz, Liechtenstein.
Department for Finance (MSc Student), University of Liechtenstein, Vaduz, Liechtenstein.
ABSTRACT
This paper tries to make a comparison and connection between Fokker-Planck or forward Kolmogorov equation and psychological future time which is based on quantum mechanics. It will be showed that in quantum finance forward interest rate model can be further improved by noting that the predicted correlation structure for field theory models depends only on variable where t is present time and x is future time. On the other side, forward Kolmogorov equation is a parabolic partial differential equation, requiring international conditions at time t and to be solved for . The aforementioned equation is to be used if there are some special states now and it is necessary to know what can happen later. It will be tried to establish the connection between these two equations. It is proved that the psychological future time if applied and implemented in Fokker-Planck equation is unstable and is changeable so it is not easily predictable. Some kinds of nonlinear functions can be applied in order to establish the notion of psychological future time, however it is unstable and it should be continuously changed.
This paper tries to make a comparison and connection between Fokker-Planck or forward Kolmogorov equation and psychological future time which is based on quantum mechanics. It will be showed that in quantum finance forward interest rate model can be further improved by noting that the predicted correlation structure for field theory models depends only on variable where t is present time and x is future time. On the other side, forward Kolmogorov equation is a parabolic partial differential equation, requiring international conditions at time t and to be solved for . The aforementioned equation is to be used if there are some special states now and it is necessary to know what can happen later. It will be tried to establish the connection between these two equations. It is proved that the psychological future time if applied and implemented in Fokker-Planck equation is unstable and is changeable so it is not easily predictable. Some kinds of nonlinear functions can be applied in order to establish the notion of psychological future time, however it is unstable and it should be continuously changed.
KEYWORDS
Psychological Future Time, Fokker-Planck Equation, Kolmogorov Forward Equation, Lagrangian, Nonlinear Future Time
Psychological Future Time, Fokker-Planck Equation, Kolmogorov Forward Equation, Lagrangian, Nonlinear Future Time
Cite this paper
Vukovic, O. (2015) On the Application of Fokker-Planck Equation to Psychological Future Time. Open Journal of Applied Sciences, 5, 571-575. doi: 10.4236/ojapps.2015.510055.
Vukovic, O. (2015) On the Application of Fokker-Planck Equation to Psychological Future Time. Open Journal of Applied Sciences, 5, 571-575. doi: 10.4236/ojapps.2015.510055.
References
[1] Baaquie, B.E. (2004) Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/cbo9780511617577 [2] Baaquie, B.E. and Martin, F. (2007) Quantum Psyche: Quantum Field Theory of the Human Psyche. NeuroQuantology, 3. http://dx.doi.org/10.14704/nq.2005.3.1.57 [3] Janssen, H.K. (1976) On a Lagrangean for Classical Field Dynamics and Renormalization Group Calculations of Dynamical Critical Properties. Zeitschrift für Physik B Condensed Matter, 23, 377-380.
http://dx.doi.org/10.1007/BF01316547 [4] Risken, H. (1984) Fokker-Planck Equation. Springer Berlin Heidelberg, Berlin, 63-95.
http://dx.doi.org/10.1007/978-3-642-96807-5_4 [5] Wilmott, P. (2013) Paul Wilmott on Quantitative Finance. John Wiley & Sons, Hoboken.
[1] Baaquie, B.E. (2004) Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/cbo9780511617577 [2] Baaquie, B.E. and Martin, F. (2007) Quantum Psyche: Quantum Field Theory of the Human Psyche. NeuroQuantology, 3. http://dx.doi.org/10.14704/nq.2005.3.1.57 [3] Janssen, H.K. (1976) On a Lagrangean for Classical Field Dynamics and Renormalization Group Calculations of Dynamical Critical Properties. Zeitschrift für Physik B Condensed Matter, 23, 377-380.
http://dx.doi.org/10.1007/BF01316547 [4] Risken, H. (1984) Fokker-Planck Equation. Springer Berlin Heidelberg, Berlin, 63-95.
http://dx.doi.org/10.1007/978-3-642-96807-5_4 [5] Wilmott, P. (2013) Paul Wilmott on Quantitative Finance. John Wiley & Sons, Hoboken.