dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

first passage and risk evaluation under stochastic volatility we solve the first passage problem for the heston random diffusion model we obtain exact analytical expressions for the survival and the hitting probabilities to a given level of return we study several asymptotic behaviors and obtain approximate forms of these probabilities which prove among other interesting properties the nonexistence of a mean first passage time one significant result is the evidence of extreme deviations which implies a high risk of default when certain dimensionless parameter related to the strength of the volatility fluctuations increases we confront the model with empirical daily data and we observe that it is able to capture a very broad domain of the hitting probability we believe that this may provide an effective tool for risk control which can be readily applicable to real markets both for portfolio management and trading strategies

modularity in orbifold theory for vertex operator superalgebras this paper is about the orbifold theory for vertex operator superalgebras given a vertex operator superalgebra v and a finite automorphism group g of v we show that the trace functions associated to the twisted sectors are holomorphic in the upper half plane for any commuting pairs in g under the c2 cofinite condition we also establish that these functions afford a representation of the full modular group if v is c2 cofinite and g rational for any g g

superstatistical fluctuations in time series applications to share price dynamics and turbulence we report a general technique to study a given experimental time series with superstatistics crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration the proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions we test the method thoroughly with surrogate data sets then the applicability of the superstatistical approach is illustrated using real experimental data we study two examples velocity time series measured in turbulent taylor couette flows and time series of log returns of the closing prices of some stock market indices

q gaussian diffusion in stock markets we analyze the standard poor s 500 stock market index from the past 22 years the probability density function of price returns exhibits two well distinguished regimes with self similar structure the first one displays strong superdiffusion together with short time correlations and the second one corresponds to weak superdiffusion with weak time correlations both regimes are well described by q gaussian distributions the porous media equation a special case of the tsallis bukman equation is used to derive the governing equation for these regimes and the black scholes diffusion coefficient is explicitly obtained from the governing equation

a musta scheme for a nonconservative two fluid model we present a multistage centered scheme of the kind proposed by toro appl numer math 56 2006 pp 1464 1479 for numerically resolving the simultaneous flow of two fluids through a transport pipeline this model contains nonconservative terms in both the temporal and spatial derivatives and an extension of the standard numerical framework for conservation laws is needed in this paper we rewrite the model in an equivalent mathematical form eliminating the nonconservative time derivatives this allows us to use the framework described by pares siam j numer anal 44 2006 pp 300 321 we develop force and musta type schemes which are consistent with pares formalism numerical simulations demonstrate a high degree of stability of our proposed schemes comparisons with the roe and rusanov schemes indicate that convergence to near identical solutions is obtained when the nonconservative terms are discretized with respect to the same evaluation of the path dependent integrals however if the schemes are not mutually formally path consistent in the sense of pares different converged solutions are obtained

superstatistical fluctuations in time series of leverage returns abstract we analyze to what extent the emergence of fat tailed q gaussian distributions of daily leverage returns of north american industrial companies that survive default and de listing between 2006 and 2012 can be described by superstatistics to this end we compare mean values of the tsallis entropic parameter q obtained by two independent methods i direct fitting of q gaussians to distributions of leverage returns and ii derived from shape parameters of gamma distributions fitted to histograms of inverted realized variances of these returns for a vast majority of companies we observe the striking consistency of average values of q obtained by both methods this finding supports the applicability of superstatistical hypothesis which assumes that q gaussians result from the superposition of locally normal distributions with gamma distributed precision inverted variance

topological data analysis of financial time series landscapes of crashes abstract we explore the evolution of daily returns of four major us stock market indices during the technology crash of 2000 and the financial crisis of 2007 2009 our methodology is based on topological data analysis tda we use persistence homology to detect and quantify topological patterns that appear in multidimensional time series using a sliding window we extract time dependent point cloud data sets to which we associate a topological space we detect transient loops that appear in this space and we measure their persistence this is encoded in real valued functions referred to as a persistence landscapes we quantify the temporal changes in persistence landscapes via their l p norms we test this procedure on multidimensional time series generated by various non linear and non equilibrium models we find that in the vicinity of financial meltdowns the l p norms exhibit strong growth prior to the primary peak which ascends during a crash remarkably the average spectral density at low frequencies of the time series of l p norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03 10 2000 or to the lehman bankruptcy on 09 15 2008 our study suggests that tda provides a new type of econometric analysis which complements the standard statistical measures the method can be used to detect early warning signals of imminent market crashes we believe that this approach can be used beyond the analysis of financial time series presented here

vertex operators and symmetric functions an algorithm for the calculation of q dependent spin characters of the symmetric group is given with an explicit example of s4 a method for constructing the q analogue of the vertex operators is developed a 1 1 correspondence between the space v of twisted q vertex operators and the ring of q deformed symmetric functions lambda x zq q t is established and a mapping from v to lambda x zq q t is defined a number of relevant theorems are given

default risk modeling beyond the first passage approximation extended black cox model we develop a generalization of the black cox structural model of default risk the extended model captures uncertainty related to firm s ability to avoid default even if company s liabilities momentarily exceeding its assets diffusion in a linear potential with the radiation boundary condition is used to mimic a company s default process the exact solution of the corresponding fokker planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative grade ratings with varying time to maturity introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons which is the key advantage of the proposed model we also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for nonzero credit spreads for bonds with very short time to maturity

2 permutations of lattice vertex operator algebras higher rank abstract this paper is a continuation of our investigation on 2 permutation of lattice vertex operator algebras in particular the quantum dimensions of irreducible modules and the fusion rules are determined if the rank of the lattice is one these results have been obtained previously in 27

microscopic origin of non gaussian distributions of financial returns abstract in this paper we study the possible microscopic origin of heavy tailed probability density distributions for the price variation of financial instruments we extend the standard log normal process to include another random component in the so called stochastic volatility models we study these models under an assumption akin to the born oppenheimer approximation in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process in this approximation we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero drift modified log returns we verify that the dow jones industrial average index indeed follows this scaling we then focus on two popular stochastic volatility models the heston and hull white models in particular we show that in the hull white model the resulting probability distribution of log returns in this approximation corresponds to the tsallis t student distribution the tsallis parameters are given in terms of the microscopic stochastic volatility model finally we show that the log returns for 30 years dow jones index data is well fitted by a tsallis distribution obtaining the relevant parameters

pursuing the double affine grassmannian i transversal slices via instantons on a_k singularities this article is the first in a series that describes a conjectural analog of the geometric satake isomorphism for an affine kac moody group for simplicity we only consider the untwisted and simply connected case here the usual geometric satake isomorphism for a reductive group g identifies the tensor category rep g of finite dimensional representations of the langlands dual group g with the tensor category pervg o grg of g o equivariant perverse sheaves on the affine grassmannian grg g k g o of g here k c t and o c t as a by product one gets a description of the irreducible g o equivariant intersection cohomology ic sheaves of the closures of g o orbits in grg in terms of q analogs of the weight multiplicity for finite dimensional representations of g the purpose of this article is to try to generalize the above results to the case when g is replaced by the corresponding affine kac moody group gaff we refer to the not yet constructed affine grassmannian of gaff as the double affine grassmannian more precisely in this article we construct certain varieties that should be thought of as transversal slices to various gaff o orbits inside the closure of another gaff o orbit in grgaff we present a conjecture that computes the intersection cohomology sheaf of these varieties in terms of the corresponding q analog of the weight multiplicity for the langlands dual affine group gaff and we check this conjecture in a number of cases some further constructions such as convolution of the corresponding perverse sheaves analog of the beilinson drinfeld grassmannian and so forth will be addressed in another publication

model for non gaussian intraday stock returns stock prices are known to exhibit non gaussian dynamics and there is much interest in understanding the origin of this behavior here we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations called intraday returns and verify the model using a large database for several stocks traded on the london stock exchange we provide evidence that the return distribution for these stocks is non gaussian and similar in shape and that the distribution appears stable over intraday time scales we explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution this produces returns that are student distributed for intraday time scales the predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution

transition from lognormal to χ2 superstatistics for financial time series abstract share price returns on different time scales can be well modelled by a superstatistical dynamics here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales it is shown that while 2 superstatistics works well on a time scale of days on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics the system dynamics thus exhibits a transition from lognormal to 2 superstatistics as a function of time scale we discuss a more general model interpolating between both statistics which fits the observed data very well we also present results on correlation functions of the extracted superstatistical volatility parameter which exhibits exponential decay for returns on large time scales whereas for returns on small time scales there are long range correlations and power law decay

on alternative q weibull and q extreme value distributions properties and applications abstract tsallis statistics and tsallis distributions have been attracting a significant amount of research work in recent years importantly the tsallis statistics q distributions have been applied in different disciplines yet a relationship between some existing q weibull distributions and q extreme value distributions that is parallel to the well established relationship between the conventional weibull and extreme value distributions through a logarithmic transformation has not be established in this paper we proposed an alternative q weibull distribution that leads to a q extreme value distribution via the q logarithm transformation some important properties of the proposed q weibull and q extreme value distributions are studied maximum likelihood and least squares estimation methods are used to estimate the parameters of q weibull distribution and their performances are investigated through a monte carlo simulation study the methodologies and the usefulness of the proposed distributions are illustrated by fitting the 2014 traffic fatalities data from the national highway traffic safety administration

an extremal mathcal n 2 superconformal field theory here we provide an example of an extremal chiral mathcal n 2 superconformal field theory at c 24 the construction is based on a mathbb z 2 orbifold of the theory associated to the a 1 24 niemeier lattice the statespace is governed by representations of the sporadic group m 23

calculus of twisted vertex operators starting from an arbitrary isometry of an arbitrary even lattice twisted and shifted vertex operators are introduced under commutators these operators provide realizations of twisted affine lie algebras this construction generalizing a number of known ones is based on a self contained calculus

fractional step methods for thermohydraulic calculation abstract a method of fractional steps is used to extend a semi implicit finite difference technique for multidimensional two phase flow calculations this extension permits time step size to be chosen independent of convection velocities in one space direction and still resolves multidimensional coupled sonic and phase exchange effects implicitly by forming a simple poisson problem for pressure because pure time splitting by physical phenomena was found unsuited to thermal hydraulics problems a stabilizing corrections method was chosen an application in nuclear reactor safety analysis is demonstrated

the compressible euler equations in a bounded domain existence of solutions and the incompressible limit a short time existence theorem is proven for the euler equations for nonisentropic compressible fluid flow in a bounded domain and solutions with low mach number and almost incompressible initial data are shown to be close to corresponding solutions of the equations for incompressible flow

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

nonlinear generalized functions and jump conditions for a standard one pressure liquid gas model abstract the mixture of a liquid and a gas is classically represented by one pressure models these models are a system of pdes in nonconservative form and shock wave solutions do not make sense within the theory of distributions they give rise to products of distributions that are not defined within distribution theory but they make sense by applying a theory of nonlinear generalized functions to these equations in contrast to the familiar case of conservative systems the jump conditions cannot be calculated a priori jump conditions for these nonconservative systems can be obtained using the theory of nonlinear generalized functions by inserting some adequate physical information into the equations the physical information that we propose to insert for the one pressure models of a mixture of a liquid and a gas is a natural mathematical expression in the theory of nonlinear generalized functions of the fact that liquids are practically incompressible while gases are very compressible and so they do not satisfy equally well their respective state laws on the shock waves this modelization gives well defined explicit jump conditions the great numerical difficulty for solving numerically nonconservative systems is due to the fact that slightly different numerical schemes can give significantly different results the jump conditions obtained above permit to select the numerical schemes and validate those that give numerical solutions that satisfy these jump conditions which can be an important piece of information in the absence of other explicit discontinuous solutions and of precise observational results we expose with care the mathematical originality of the theory of nonlinear generalized functions an original abstract analysis issued by the leopoldo nachbin team on infinite dimensional holomorphy that permits to state mathematically physical facts that cannot be formulated within distribution theory and are the key for the removal of ambiguities that classically appear when one tries to calculate on multiplications of distributions that occur in the differential equations of physics

graphene lattice field theory and symmetries borrowing ideas from tight binding model we propose a board class of lattice field models that are classified by non simply laced lie algebras in the case of an 1 su n series we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice lsun are governed by the complex fundamental representations n and n of su n and the second nearest neighbor interactions are described by its adjoint n n the lattice models associated with the leading su 2 su 3 and su 4 cases are explicitly studied and their fermionic field realizations are given it is also shown that the su 2 and su 3 models describe the electronic properties of the acetylene chain and the graphene respectively it is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the an roots through the typical dependence n 2 roots cosk with k the wave vector other features such as the so 2n extension and other application

a nearly implicit hydrodynamic numerical scheme for two phase flows this article presents an extension of the semi implicit numerical scheme for two phase flow simulation the extension uses an implicit evaluation of the convective fluxes and thus eliminates the material courant stability restriction the new algorithm involves a two step approach for the mass and energy equations and a single fully implicit step for the momentum evaluations some analysis and accuracy considerations for the scheme are also presented

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

a stability enhancing two step method for fluid flow calculations an extension is presented of semi implicit methods such as the implicit continuous eulerian ice technique for modeling fluid flow this new approach eliminates the material courant stability limit associated with semi implicit methods at little additional computational cost

q gaussian distributions of leverage returns first stopping times and default risk valuations a b s t r a c t we study the probability distributions of daily leverage returns of 520 north american industrial companies that survive de listing during the financial crisis 2006 2012 we provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of q gaussian distributions with the tsallis entropic parameter within the interval 1 q 2 the fat tails of the observed distributions imply a much higher probability of extreme movements in a company s leverage ratio than forecasted by the normal distribution q 1 motivated by these findings we develop a q gaussian generalization of traditional structural models of default derived exact analytical expressions for the probability distribution of a first stopping time and its intensity forecast significantly higher probability of default and much wider credit spreads at short time horizons our findings are broadly consistent with the results of empirical studies in equity markets and are essential for single name default forecasting as well as valuations of portfolio credit risk and economic capital which might be underestimated by a classic theory of diversified portfolio optimization

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

on mathbb z _p z p orbifold constructions of the moonshine vertex operator algebra for p 3 5 7 13 we consider a mathbb z p orbifold construction of the moonshine vertex operator algebra v natural we show that the vertex operator algebra obtained by the mathbb z p orbifold construction on the leech lattice vertex operator algebra v lambda and a lift of a fixed point free isometry of order p is isomorphic to the moonshine vertex operator algebra v natural we also describe the relationship between those mathbb z p orbifold constructions and the mathbb z 2 orbifold construction in a uniform manner in appendix we give a characterization of the moonshine vertex operator algebra v natural by the existence of an orthogonal pair of ising vectors

escape problem under stochastic volatility the heston model we solve the escape problem for the heston random diffusion model from a finite interval of span l we obtain exact expressions for the survival probability which amounts to solving the complete escape problem as well as for the mean exit time we also average the volatility in order to work out the problem for the return alone regardless of volatility we consider these results in terms of the dimensionless normal level of volatility a ratio of the three parameters that appear in the heston model and analyze their form in several asymptotic limits thus for instance we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level we compare our results with those of the wiener process and show that the assumption of stochastic volatility in an apparently paradoxical way increases survival and prolongs the escape time we finally observe that the model is able to describe the main exit time statistics of the dow jones daily index

asymptotic study of the initial value problem to a standard one pressure model of multifluid flows in nondivergence form abstract we construct families of approximate solutions to the initial value problem and provide complete mathematical proofs that they tend to satisfy the standard system of isothermal one pressure two fluid flows in 1 d when the data are l 1 in densities and l in velocities to this end we use a method that reduces this system of pdes to a family of systems of four odes in banach spaces whose smooth solutions are these approximate solutions this method is constructive using standard numerical methods for odes one can easily and accurately compute these approximate solutions which therefore from the mathematical proof can serve for comparison with numerical schemes one observes agreement with previously known solutions from scientific computing evje and flatten 2003 16 we show that one recovers the solutions of these authors exactly in one case with a slight difference in another case then we propose an efficient numerical scheme for the original system of two fluid flows and show it gives back exactly the same results as the theoretical solutions obtained above