Quantum Financial Economics - Essay Example

Heisenberg Uncertainty Principle in Economics Introduction One thing that cannot be left unmentioned in economics is the aspect of uncertainty because of the economic measurements such as quantity, time, etc. These arise out of inaccurate measurements and lack of a 100% appropriate verifiability of any given data. This uncertainty can be well explained by looking at the Heisenberg Uncertainty Principle in physics. The uncertainty principle has it that the velocity/momentum and position cannot be measured both, exactly, simultaneous (actually pairs of energy, position and time). This principle emanates from the measurement difficulty, the intimate linkage amid the particle and wave nature of quantum objects (Hilgevoord, 2005, pp. 29-30). Normally, the change in momentum of a particle turns out more ill defined as the function of wave is confined to a lesser region. The nature of the wave to particles implies a particle is a wave package, the composite of a number of waves. A number of waves refer to many momentums; only one momentum can be made by observation out of many. The exact facts of complimentary pairs (time, energy, position) are impossible. For instance, it is possible to measure an electron’s position, but not its energy (momentum) simultaneously. Complementarity also implies that dissimilar experiments results into dissimilar outcomes (such as the two slit experiment). Thus, a single reality at the quantum level cannot be applied. Mathematically the uncertainty principle can be described as follows, where p is momentum and x is position: ∆x X ∆p> ħ/2π (Romanovsky & Romanovsky, 2007, pp. 114-116). It fundamentally shows that the mixture of the error in momentum times the error in position should usually be bigger than Planck’s constant. Therefore, it is possible to measure an electron’s position to some accuracy; however, its momentum will appear in a bigger range of values. Similarly, it is possible to measure an electron’s momentum accurately; however, its position remains unidentified at that particular time (Romanovsky & Romanovsky, 2007, pp. 113-114). It is evident that there is uncertainty in modeling, foretelling and interpretation of prevailing socio-economic circumstances. This can be visible in the global financial systems’ instability, depending on natural and ordinary disturbances in the contemporary markets and greatly undesirable financial crises (Hilgevoord, 2005, pp. 30-36). This brings the necessity of not only researching on uncertainty in economics, but also establishing the connection to the Heisenberg’s uncertainty principle. As observed above the form of uncertainty here can be referred to as the economic uncertainty principle. Economic uncertainty principle In economics, future events may be regarded as, at least partly, uncertain. This partial uncertainty or uncertainty may be hardly noticeable, invisible. In general this principle shows that a number of future events carry a degree of uncertainty. There are evident and concealed, latent uncertainties. Taking into account evident uncertainties is, really, clear and unimportant and often not useful. The fundamental although not the sole goal of this uncertainty is to take into account concealed, latent uncertainties. Therefore, future events contain to some extent a degree of (concealed) uncertainty. It should be underscored that in some instances, an influence of the economic uncertainty principle can be ignored. In other instances, it will enhance an accuracy of calculations. Still in other instances, it will be necessary, even vital. The important development to note is that application of this principle has the effect of enhancing the precision of the economic theory. The principle may be, in a way, treated in terms of asymmetric or incomplete information. There exist evident analogies amid uncertainty principle of Heisenberg and Einstein’s specific and general theories of relativity on side A and the uncertainty principle in economics on side B (Isaacson, 2007, pp. 76-78). The influence of the great physicians on the principle cannot be unnoticed. Furthermore, the new principle can be, to some level, the result of the uncertainty principle by Heisenberg. In fact, one cannot measure at the same time both position and impulse better that with uncertainty. ∆x X ∆p≥h/2π Where ∆x = position uncertainty ∆p =impulse uncertainty ħ =Planck’s constant under division by 2π (Soloviev, 2008, pp.124-126). The implication here together with real impossibility to know the reasons and genesis of future events, can result into uncertainties of future events. The circumstance, when making a comparison of the economic theory with and without the new principle of uncertainty, is in logically analogous to the circumstance when making a comparison between quantum and classical physics. Classical economists do not factor in the economic uncertainty process. For instance, here are two processes: One which is a fundamental one for economics – a selection of a result which probability is X, and another which is a fundamental one for physics -on a barrier where there is scattering of which the height is Y. In the two processes, when the uncertainty is vital: For high X and Y the selections as well as scattering of barriers are lower than the classical theory’s; For low X and Y the selections as well as the scattering of the barrier are higher than the classical theory’s. Particular economic uncertainty principle The particular economic uncertainty principle stresses one uncertain dimension of future events, which is probability. It says that future events’ probabilities are, to some level, uncertain. This level may be hardly noticeable, invisible. It may be very vital, if not considerable. Most of the future events have, at least, a level of uncertainty. This principle of economic uncertainty appears as follows: A future event’s probability has, at least, a level of concealed uncertainty. Or in other words, every future event’s probability has, at least, a level of concealed uncertainty. Mathematically, this can be expressed as follows: a. Y̴Ypreliminary + ∆+Y (Scircumstance; Ypreliminary)-∆Y(Scircumstance; Ypreliminary) Where Y=the value of actual or future probability, Ypreliminary =the preliminary determined Y, ∆+Y = the portion of uncertainty of probability, which increases Y, Scircumstance = a set of the circumstance’s parameters, ∆Y=the portion of uncertainty of probability, which decreases Y. Or, this can be reduced as follows: a. Y̴Ypreliminary +-∆Y(Scircumstance; Ypreliminary) (Goncalves, 2011, p. 112) Where ∆Y = + ∆+Y and -∆_Y The next b. Ymean=Ypreliminary + ᵟY(Scircumstance; Ypreliminary) Where Ymean =the mean value of Y a. ᵟY =the Change, the mean value of future or real Y’s bias in the making of comparison with the preliminary determined Y’s value (ᵟY might be as negative or positive) (Hedenmalm, 2012, pp. 697-702) Considering a case where Yhigh preliminary =99% Ymedium preliminary=50% Ypreliminary=1% and Yhigh mean1% Using equation (b) Ymean=Ypreliminary + ᵟY In a general form the equation can be written as follows: a. ᵟYhigh 0 Where this becomes High = regards the Ypreliminary (and corresponding Y), such as (100% - Ypreliminary) is small when comparing with ∆+Y Where it becomes Medium = concerns to Ypreliminary (and corresponding Y), that belongs to the medium that ranges 0% to 100% where ᵟY̴0, Low =refers to Ypreliminary (and corresponding Y), such as Ypreliminary is minute when comparing with ∆Y Or (b) Yhigh mean = Yhigh preliminary - lᵟY l Ylow preliminary Or, can be made simple as follows (a) Yhigh mean Ylow preliminary (Hedenmalm, 2012, pp. 691-696) Application of Economic uncertainty principle 1. Risk aversion, Allais paradox, Overweighting of low probabilities Some of the initial problems that can be explained include, risk aversion, the Ellsberg paradox, Allais paradox, overweighting of low probabilities, the equity premium puzzle, loss aversion, and uniform explanation of both losses and gains. i. First kind of outcomes. High probabilities Taking into consideration an instance for probabilities that are around a 100% and assuming that a choice is offered of solely one of the following: A gamble: The win is $100 with the probability Y (preliminary) =99% or The loss of $0 with the (preliminary) probability 1% Mathematically the expectations of being sure Rsure and gambling Rgamb results are exactly identical: Rsure =$99 x 100% =$99, and Rgamb =$100 x 99% =$99, thus, $99 = $99 (Romanovsky & Romanovsky, 2007, pp. 115-18) However, the well-determined experimental truth is: in identical experiments the clear majority of individuals chose the sure win option instead of the gambling. This happens to a modification of the classical Allais paradox mentioned above. This is so, because anything can take place. The gambling may be trickery or may suffer failure. This may lead to physical and psychological torture to the parties involved because gambling can be interrupted by anybody (the authorities, any ill intention person among others). As result, the actual probabilities will be uncertain (irrespective of the preliminary ones being certain or uncertain). For instance, for, such as ᵟY=-14% and ᵟYsure =-8% and normalizing ᵟYsure to 100%. 100%-8%=92%, 99%-14%=85% 92%: 92% =100% 85%:92%=88.5% ̴ 89% Rsure =$99 x 100% =$99, and Rgamb =$100 x 89% =$89, thus, $99 = $89 (Soloviev, 2008, pp. 127-131) Thus, actually, the mathematical expectation of being sure with the results is more than the gambling result one. Thus, the selection of most of the people might correspond precisely to the mathematical expectations. Thus, the particular economic uncertainty principle as well as its first hypothesis is capable to naturally and obviously offer an explanation to this and identical analogies. Conclusion This paper has explored aspects of uncertainty principle through analyzing physical notions and their informal and formal connections with actual economic measurements. The basic tenets around the Heisenberg’s uncertainty principle have been used to show their effect on economic measurements, especially with the development of the economic uncertainty principle (Goncalves, 2011, p. 122). The procedures adopted in the discussion arise from socio-economic time series analysis as well as the interpretation of the uncertainty principle by Heisenberg. The aspect of economic Planck’s constant also came into the equation. The theory has been tested on circumstance involving probabilities and choice in the life of people. The results arrived at show that there is connection between the Heisenberg’s uncertainty principle and the new principle of economic uncertainty principle. This warrants further investigation into the economic uncertainty principle to define and offer even better explanation of the scenarios it affects economic thinking and functioning. Reference list Goncalves, P. C., 2011. Quantum Financial Economics - Risk and Returns. arXiv:1107.2562, p. 112. Hedenmalm, H., 2012. Heisenbers uncertainty principle in the sense of Beurling. J. Anal. Math, 46 (2), pp. 691-702. Hilgevoord, J., 2005. Time in quantum mechanics: a story of confusion. Studies in History and philosophy of Modern Physics, 10 (6), pp. 29-60. Isaacson, W., 2007. Einstein: His Life and Universe. New York: Simon & Schuster. pp. 76-79 Romanovsky, Y. M., and Romanovsky, M. Y., 2007. An introduction to econopysics. Statistical and dynamical models. Moscow: IKI. pp. 113-18 Soloviev, N. V., 2008. Mathematical Economics. A text book for Self-study (in Ukrainian). Cherkassy: CHNU. pp. 124-131 Read More