Quantum gambling using mesoscopic ring qubits

Quantum Game Theory provides us with new tools for practising games and some other risk related enterprices like, for example, gambling. The two party gambling protocol presented by Goldenberg {\it et al} is one of the simplest yet still hard to implement applications of Quantum Game Theory. We propose potential physical realisation of the quantum gambling protocol with use of three mesoscopic ring qubits. We point out problems in implementation of such game.Comment: 4 pages, 1 figure, poster during XXX Intern. Conf. of Theoretical Physics, Electron correlations in nano- and microsystems, Ustron 9-14 September 2006. Minor corrections, references added; to appear in physica status solidi

Giffen paradoxes in quantum market games

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history and basic ideas of quantum game theory. Description of Giffen paradoxes in this new formalism is discussed.Comment: 12 pages (2 figs), LaTe

Geometry of Financial Markets -- Towards Information Theory Model of Markets

Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the object of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset X (i.e. in units of X) are given by linear maps. Among various types of metrics that have financial interpretation, the min-max metrics on the space of quotations can be introduced. This metrics has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metrics on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.Comment: Talk given at the APFA5 Conference, Torino, 200

Kelly Criterion revisited: optimal bets

Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a explanation of this fact. Kelly's approach allows for an interesting financial interpretation of the Boltzmann/Shannon entropy. A "no-go" hypothesis for big investors is suggested.Comment: APFA5 Conference, Torino, 200

The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.Comment: APFA5 Conference, Torino, 200

Fixed point theorem for simple quantum strategies in quantum market games

A simple but nontrivial class of the quantum strategies in buying-selling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal profits in such the games is considered. The entangled merchants hypothesis is proposed.Comment: 7 pages, 1 figure; The International Econophysics Conference, Bali 200

Constraints on the optical precursor to the naked-eye burst GRB080319B from Pi of the Sky observations

I present the results of the search for an optical precursor to the naked-eye burst - GRB080319B, which reached 5.87m optical peak luminosity in the "Pi of the Sky" data. A burst of such a high brightness could have been preceded by an optical precursor luminous enough to be in detection range of our experiment. The "Pi of the Sky" cameras observed the coordinates of the GRB for about 20 minutes prior to the explosion, thus provided crucial data for the precursor search. No signal within 3 sigma limit was found. A limit of 12m (V-band equivalent) was set based on the data combined from two cameras, the most robust limit to my knowledge for this precursor.Comment: Accepted for publication in Astronomy and Astrophysics on 07 February 201

Quantum extension of European option pricing based on the Ornstein-Uhlenbeck process

In this work we propose a option pricing model based on the Ornstein-Uhlenbeck process. It is a new look at the Black-Scholes formula which is based on the quantum game theory. We show the differences between a classical look which is price changing by a Wiener process and the pricing is supported by a quantum model

Projective Market Model Approach to AHP Decision-Making

In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to projective geometry formalism and generalise it to intransitive case. We give financial interpretations of such generalised model and propose its simplification. The unification of the AHP model and projective aspect of portfolio theory suggests a wide spectrum of new applications such extended model.Comment: APFA 6 - Applications of Physics in Financial Analysis 6th International Conference, 4-7 July 2007, Lisbon, Portuga