Planimetry of Economic States

Abstract

The new information physical method of constructing the space of economic states is proposed. Unlike the existing theories of consumption, its properties are completely determined axiomatically by the operation of measurement and do not require phenomenological assumptions. The authors consider a transaction of exchange of valuables between two proprietors as such operation. The result of measurement is a dimensional number equal to the proportion of exchange. The constructed space appears to be Euclidean vector space with ordinary operators of composition of vectors, their scalar product, etc. The task of determining the parameters of equilibrium of a complex economic system can be formulated as a task of statics in the constructed space and can be solved by one of the physical methods.

D-brane solutions under market panic

“…Finally to obtain real financial dynamics of stock market full mathematical equations Eqs. (26,27) and Eq. ( 36) obtained on the spherical brane with appropriate boundary conditions need to be exactly solved.…”

“…The option prices in our model are represented by the electrons with mass M = 1/σ 2 , where sigma is volatility, as in work [20]. In contrast to other quantum models with ordinary particles [21][22][23][24][25][26], we assume an electron with spin up and down which entitles us to use some relativistic approach. Moreover, difference in spin orientation for one electron could play a key role in difference for up and down factors of increasing and decreasing option price in one step time interval of change price in discrete binomial and trinomial models [27,28].…”

Quantum effects in an expanded Black-Scholes model

“…Thus, the calculation of VIX is unambiguously formulated and (more significantly) not restricted by the usual Black-Scholes assumptions, making it more reflective of market conditions than an implied volatility based on the latter. Secondly, the formula (19) uses the prices of 30-day forward index options, and so is forward-looking. This makes it a more reliable indicator than historical volatility, since it is a measure of the future expected volatility of the index.…”

“…Several groups have used quantum mechanical concepts from the outset to obtain inherently non-classical Black-Scholes models. Broadly speaking, these studies are based either on noncommutativity (the Heisenberg picture) [17][18][19][20][21], or the Black-Scholes Hamiltonian and wave function (the Schrödinger picture) [22][23][24][25][26]. Here, our focus is on the work of Segal and Segal [17], who introduced quantum effects into the Black-Scholes model to incorporate market features such as the impossibility of simultaneously measuring prices and their instantaneous forward time derivatives.…”

Emergent quantum mechanics of finances

“…In the last decades there were performed numerous investigations on applying quantum mechanics to financial markets, in particular secondary financial markets (see e.g. [1][2][3][4][5][6][7][8] and book [9], and many publications in arxiv.org). Unfortunately, the constructing of quantum theory of finances often reduces to simple postulation of the Schrödinger equation and its subsequent solution under some entry conditions.…”