estimating the covariance matrix by signal subspace averaging an efficient algorithm is presented for estimating a covariance matrix consisting of a low rank signal term and a full rank noise term known apart from a scalar factor for each sample of the vector of sensor outputs the algorithm approximates in the least squares sense a rank one update of the covariance matrix under the side condition that the rank of the signal term remains bounded if the model noise is spatially colored the least squares approximation is preceded by spatial prewhitening it is shown that if the rank of the signal term is small compared to the number of sensors then the proposed algorithm requires substantially less computational work than conventional averaging some simulation results are included indicating that the proposed algorithm reduces the variance of some commonly used spectral estimators in off target directions without impairing their detection and resolution properties

emergence of fuzzy preferences for risk in a birkhoff von neumann logics environment we show that if a portfolio of a financial derivative asset and a stock is put in an environment where the value of an asset besides its price is formalized as a superposition of price states such portfolio may not be risk free and fuzzy preferences for risk premia may exist we argue for a modification of the classical brownian motion process as used in option pricing this modification on the classical brownian motion we call the email protected brownian motion and one specific format of this email protected brownian motion can be shown to have a connection with the quantum physical schrodinger equation

quantum bohmian model for financial market we apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market the hamiltonian formalism on the price price change phase space describes the classical like evolution of prices this classical dynamics of prices is determined by hard conditions natural resources industrial production services and so on these conditions are mathematically described by the classical financial potential v q where q q1 qn is the vector of prices of various shares but the information exchange and market psychology play important and sometimes determining role in price dynamics we propose to describe such behavioral financial factors by using the pilot wave bohmian model of quantum mechanics the theory of financial behavioral waves takes into account the market psychology the real trajectories of prices are determined through the financial analogue of the second newton law by two financial potentials classical like v q hard market conditions and quantum like u q behavioral market conditions

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

option pricing stochastic volatility singular dynamics and constrained path integrals abstract stochastic volatility models have been widely studied and used in the financial world the heston model heston 1993 7 is one of the best known models to deal with this issue these stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter which relates the two brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset solutions to the heston model in the context of option pricing using a path integral approach are found in lemmens et al 2008 21 while in baaquie 2007 1997 12 13 propagators for different stochastic volatility models are constructed in all previous cases the propagator is not defined for extreme cases 1 it is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator in this paper we study in detail a general class of stochastic volatility models for extreme values 1 and show that in these two cases the associated classical dynamics corresponds to a system with second class constraints which must be dealt with using dirac s method for constrained systems dirac 1958 1967 22 23 in order to properly obtain the propagator in the form of a euclidean hamiltonian path integral henneaux and teitelboim 1992 25 after integrating over momenta one gets an euclidean lagrangian path integral without constraints which in the case of the heston model corresponds to a path integral of a repulsive radial harmonic oscillator in all the cases studied the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral

a black scholes schrodinger option price bit versus qubit abstract the celebrated black scholes differential equation provides for the price of a financial derivative the uncertainty environment of such option price can be described by the classical bit a system with two possible states this paper argues for the introduction of a different uncertainty environment characterized by the so called qubit we obtain an information based option price and discuss the differences between this option price and the classical option price

a discussion on embedding the black scholes option pricing model in a quantum physics setting abstract in this paper we consider the implications of embedding the black scholes option pricing model within a quantum physical setting the option price is considered to be a state function and a potential function is found which allows the option price to satisfy the schrodinger differential equation once this arbitrage free potential function is obtained we argue for the construction of a so called arbitrage potential function this functional is instrumental in determining the existence of a financial state function we show the existence of an arbitrage free price when the potential function converges to one the existence of arbitrage hinges on the non zero value of the planck constant this constant is then linked to a parameter which regulates the probability of occurence of strategy paths we call this parameter the belief parameter we argue that it is the belief parameter which may indeed proxy arbitrage the outcome of this paper shows that the black scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

subjective modelling of supply and demand the minimum of fisher information solution abstract two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand supply profiles if one considers closing of a position as a random process we would like to present the analysis of a subjectivity in such trading models in our model the trader gets the maximal profit intensity when the probability of transaction is 0 5853 we also present a comparison with the model based on the maximum of entropy principle to the best of our knowledge this is one of the first analyses that show a concrete situation in which trader profit optimal value is in the class of price negotiating algorithms strategies resulting in non monotonic demand supply curves of the rest of the world a collective opponent our model suggests that there might be a new class of rational trader strategies that almost neglects the supply demand profile of the market this class emerges when one tries to minimize the information that strategies reveal

tracking of signal subspace projectors a new subspace tracking approach that directly operates on the projection matrix onto the signal subspace instead of tracking its unitary eigenbasis is proposed therefore the difficulties arising from introducing a calculus on the manifold of projection matrices are overcome by a proper parameterization of the projectors simulation results are presented from the field of angular frequency retrieval in array signal processing

black scholes schrodinger zipf mandelbrot model framework for improving a study of the coauthor core score abstract the data and findings by miskiewicz 2013 on the relationship between the number j of publications ranked according to their decreasing importance for some scientist with her his coauthors ca i e j 1 r as found in ausloos 2013 when specific types of publications i e proceedings in a generalized sense and peer review journals are considered are reexamined along the zipf mandelbrot law mandelbrot 1977 i e j 1 r the statistics are much improved the exponent and are compared the m a core value i e the core number of cas 1 is unaffected of course a black scholes schrodinger model framework is proposed to describe the findings

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

multi asset black scholes model as a variable second class constrained dynamical system abstract in this paper we study the multi asset black scholes model from a structural point of view for this we interpret the multi asset black scholes equation as a multidimensional schrodinger one particle equation the analysis of the classical hamiltonian and lagrangian mechanics associated with this quantum model implies that in this system the canonical momentums cannot always be written in terms of the velocities this feature is a typical characteristic of the constrained system that appears in the high energy physics to study this model in the proper form one must apply dirac s method for constrained systems the results of the dirac s analysis indicate that in the correlation parameters space of the multi assets model there exists a surface called the kummer surface k where the determinant of the correlation matrix is null on which the constraint number can vary we study in detail the cases with n 2 and n 3 assets for these cases we calculate the propagator of the multi asset black scholes equation and show that inside the kummer k surface the propagator is well defined but outside k the propagator diverges and the option price is not well defined on k the propagator is obtained as a constrained path integral and their form depends on which region of the kummer surface the correlation parameters lie thus the multi asset black scholes model is an example of a variable constrained dynamical system and it is a new and beautiful property that had not been previously observed

pilot assisted channel estimation based on second order statistics a survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements the slowly varying channel properties are described by the channel s second order statistics first a detailed comparison of classical linear pilot based channel estimators a novel matched filter and reduced rank rr approaches is made in a common framework with respect to the model they assume for the channel their performance mse and complexity the matched filter channel estimator is introduced which exploits second order statistics with quadratic order of complexity for flat correlated rayleigh fading channels an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided it is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal to noise ratio snr range the effects of these approaches on linear equalization are briefly discussed in the context of direct sequence code division multiple access ds cdma where the focus is on a generalization of the rake receiver in space and time which reduces the channel rank based on its second order statistics resulting in a complexity reduction of the equalizer for this discussion a new notation for the generalized rake is presented which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation we conclude that exploiting second order channel statistics results in significant performance gains and rr channel estimation should only be used together with equalization in the reduced signal subspace

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

cohomology of exact categories and non additive sheaves abstract we use non additive sheaves to introduce an absolute notion of hochschild cohomology for exact categories as ext s in a suitable bisheaf category we compare our approach to various definitions present in the literature

a novel analytical technique for the solution of time fractional ivancevic option pricing model abstract the ivancevic option pricing model is an alternative of the standard black scholes pricing equation which signifies a controlled brownian motion related to the nonlinear schrodinger equation even though many researchers have studied the applicability and practicality of this model but the analytical approach of this model is rarely found in the literature in this paper a novel semi analytical technique called fractional reduced differential transform method has been applied to solve the schrodinger type option pricing model which is characterized by the time fractional derivative two problems are explained to validate and prove the effectiveness of the proposed technique obtained results are compared with the solution of other existing methods for a particular case this comparison shows that the attained results are in good agreement with the existing solutions

a finite dimensional quantum model for the stock market abstract we present a finite dimensional version of the quantum model for the stock market proposed in c zhang and l huang a quantum model for the stock market physica a 389 2010 5769 our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical formalism used in the case of the quantum systems with finite dimensional hilbert space the rate of return is a discrete variable corresponding to the coordinate in the case of quantum systems and the operator of the conjugate variable describing the trend of the stock return is defined in terms of the finite fourier transform the stock return in equilibrium is described by a finite gaussian function and the time evolution of the stock price directly related to the rate of return is obtained by numerically solving a schrodinger type equation

the black scholes pricing formula in the quantum context a natural explanation for extreme irregularities in the evolution of prices in financial markets is provided by quantum effects the lack of simultaneous observability of relevant variables and the interference of attempted observation with the values of these variables represent such effects these characteristics have been noted by traders and economists and appear intrinsic to market dynamics this explanation is explored here in terms of a corresponding generalization of the wiener process and its role in the black scholes merton theory the differentiability of the wiener process as a sesquilinear form on a dense domain in the hilbert space of square integrable functions over wiener space is shown and is extended to the quantum context this provides a basis for a corresponding generalization of the ito theory of stochastic integration an extension of the black scholes option pricing formula to the quantum context is deduced

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

quantum probability and financial market can the mathematical formalism of quantum mechanics and in particular quantum probability be applied outside of physics the answer is positive in this paper we apply methods of quantum mechanics for mathematical modelling of price dynamics of the financial market we propose to describe behavioral financial factors e g expectations of traders by using the pilot wave bohmian model of quantum mechanics on the one hand our bohmian model is a quantum like model for the financial market cf with works of w segal i e segal e haven e w piotrowski j sladkowski on the other hand since bohmian mechanics provides for the possibility to describe individual price trajectories it belongs to the domain of extended research on deterministic dynamics for financial assets our model emphasizes the complexity of the financial market the traditional description of price dynamics is completed by schrodinger s dynamics for the pilot wave of expectations of traders this is a kind of socio economic model for the financial market

quantum model for the price dynamics the problem of smoothness of trajectories we apply methods of quantum mechanics to mathematical modelling of price dynamics in a financial market we propose to describe behavioral financial factors e g expectations of traders by using the pilot wave bohmian model of quantum mechanics our model is a quantum like model of the financial market cf with works of w segal i e segal e haven in this paper we study the problem of smoothness of price trajectories in the bohmian financial model we show that even the smooth evolution of the financial pilot wave t x representing expectations of traders can induce jumps of prices of shares

detection of number of sources via exploitation of centro symmetry property forward backward fb averaging is a technique which can be employed in sensor array signal processing for exploiting a so called centro symmetry property of the signal subspace to improve parameter estimation accuracy although fb averaging effectively doubles the number of data samples it also introduces correlation among these data vectors this correlation complicates not only the performance analysis but also the detection of the number of sources when fb averaging is employed existing detection procedures such as sequential hypothesis sh likelihood ratio tests minimum description length mdl and an information criterion aic must be modified to correctly account for this preprocessing of the data herein proper exploitation of the centro symmetry property of the fb averaged covariance is described and a rigorous analysis is conducted it is shown that the general scheme of existing methods is still applicable to the fb averaging case but that the parameters e g degrees of freedom need to be adjusted

dynamic optimization and its relation to classical and quantum constrained systems abstract we study the structure of a simple dynamic optimization problem consisting of one state and one control variable from a physicist s point of view by using an analogy to a physical model we study this system in the classical and quantum frameworks classically the dynamic optimization problem is equivalent to a classical mechanics constrained system so we must use the dirac method to analyze it in a correct way we find that there are two second class constraints in the model one fix the momenta associated with the control variables and the other is a reminder of the optimal control law the dynamic evolution of this constrained system is given by the dirac s bracket of the canonical variables with the hamiltonian this dynamic results to be identical to the unconstrained one given by the pontryagin equations which are the correct classical equations of motion for our physical optimization problem in the same pontryagin scheme by imposing a closed loop strategy the optimality condition for the action gives a consistency relation which is associated to the hamilton jacobi bellman equation of the dynamic programming method a similar result is achieved by quantizing the classical model by setting the wave function x t e i s x t in the quantum schrodinger equation a non linear partial equation is obtained for the s function for the right hand side quantization this is the hamilton jacobi bellman equation when s x t is identified with the optimal value function thus the hamilton jacobi bellman equation in bellman s maximum principle can be interpreted as the quantum approach of the optimization problem

a quantum model of option pricing when black scholes meets schrodinger and its semi classical limit abstract the black scholes equation can be interpreted from the point of view of quantum mechanics as the imaginary time schrodinger equation of a free particle when deviations of this state of equilibrium are considered as a product of some market imperfection such as transaction cost asymmetric information issues short term volatility extreme discontinuities or serial correlations the classical non arbitrage assumption of the black scholes model is violated implying a non risk free portfolio from haven 2002 1 we know that an arbitrage environment is a necessary condition to embedding the black scholes option pricing model in a more general quantum physics setting the aim of this paper is to propose a new black scholes schrodinger model based on the endogenous arbitrage option pricing formulation introduced by contreras et al 2010 2 hence we derive a more general quantum model of option pricing that incorporates arbitrage as an external time dependent force which has an associated potential related to the random dynamic of the underlying asset price this new resultant model can be interpreted as a schrodinger equation in imaginary time for a particle of mass 1 2 with a wave function in an external field force generated by the arbitrage potential as pointed out above this new model can be seen as a more general formulation where the perfect market equilibrium state postulated by the black scholes model represent a particular case finally since the schrodinger equation is in place we can apply semiclassical methods of common use in theoretical physics to find an approximate analytical solution of the black scholes equation in the presence of market imperfections as it is the case of an arbitrage bubble here as a numerical illustration of the potential of this schrodinger equation analogy the semiclassical approximation is performed for different arbitrage bubble forms step linear and parabolic and compare with the exact solution of our general quantum model of option pricing

pseudo hermitian formulation of the quantum black scholes hamiltonian abstract we show that the non hermitian black scholes hamiltonian and its various generalizations are pseudo hermitian the metric operator is explicitly constructed for this class of hamiltonians it is also shown that the effective black scholes hamiltonian and its partner form a pseudo supersymmetric system

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

a reactive lattice gas approach to economic cycles abstract a microscopic approach to macroeconomic features is intended a model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed a birth death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is numerically and analytically examined the reaction diffusion model can also be mapped onto a high order logistic map the role of the selection pressure along various dynamics with entity diffusion on a square symmetry lattice has been studied by monte carlo simulation the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure and to cycles the control parameter is a scalar business plan the business plan s allows for spin offs or merging and enterprise survival evolution law s whence bifurcations cycles and chaotic behavior