Long-Time Fluctuations in a Dynamical Model of Stock Market Indices

Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Levy-stable distribution L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot be expressed in a closed form, one can identify its parameters by testing the dependence of the central peak height on tau as well as the power-law decay of the tails. In an earlier study [Mantegna and Stanley, Nature 376, 46 (1995)] it was found that the behavior of the central peak of P(r) for the Standard & Poor 500 index is consistent with the Levy distribution with alpha=1.4. In a more recent study [Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found that the tails of P(r) exhibit a power-law decay with an exponent alpha ~= 3, thus deviating from the Levy distribution. In this paper we study the distribution of returns in a generic model that describes the dynamics of stock market indices. For the distributions P(r) generated by this model, we observe that the scaling of the central peak is consistent with a Levy distribution while the tails exhibit a power-law distribution with an exponent alpha > 2, namely beyond the range of Levy-stable distributions. Our results are in agreement with both empirical studies and reconcile the apparent disagreement between their results

Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements

A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda w_i(t)$ at the individual level with a global coupling through a constraint which does not allow the $w_i$'s to fall below a lower cutoff given by $c \cdot \bar w$, where $\bar w$ is their momentary average and $0<c<1$ is a constant. The dynamic variables $w_i$ are found to exhibit a power-law distribution of the form $p(w) \sim w^{-1-\alpha}$. The exponent $\alpha (c,N)$ is quite insensitive to the distribution $\Pi(\lambda)$ of the random factor $\lambda$, but it is non-universal, and increases monotonically as a function of $c$. The "thermodynamic" limit, N goes to infty and the limit of decoupled free multiplicative random walks c goes to 0, do not commute: $\alpha(0,N) = 0$ for any finite $N$ while $\alpha(c,\infty) \ge 1$ (which is the common range in empirical systems) for any positive $c$. The time evolution of ${\bar w (t)}$ exhibits intermittent fluctuations parametrized by a (truncated) L\'evy-stable distribution $L_{\alpha}(r)$ with the same index $\alpha$. This non-trivial relation between the distribution of the $w_i$'s at a given time and the temporal fluctuations of their average is examined and its relevance to empirical systems is discussed.Comment: 7 pages, 4 figure

Basic kinetic wealth-exchange models: common features and open problems

We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735], Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B 17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M. Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the equilibrium wealth distributions are proposed. The influence of heterogeneity is investigated, the appearance of the fat tail in the wealth distribution and the relaxation to equilibrium are discussed. A unified reformulation of the models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table

Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets

A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material failure, epileptic seizure intensities, and other systems. Within our theory, the large outliers are interpreted as droplets of Bose-Einstein condensate: the appearance of outliers is a natural consequence of the occurrence of Bose-Einstein condensation controlled by the relative degree of attraction, or utility, of the largest entities. For large populations, Zipf's law is recovered (except for the dragon-king outliers). The theory thus provides a parsimonious description of the possible coexistence of a power law distribution of event sizes (Zipf's law) and dragon-king outliers.Comment: Latex file, 16 pages, 1 figur

Search for lepton-flavor violation at HERA

A search for lepton-flavor-violating interactions $e p \to \mu X$ and $e p\to \tau X$ has been performed with the ZEUS detector using the entire HERA I data sample, corresponding to an integrated luminosity of 130 pb^{-1}. The data were taken at center-of-mass energies, $\sqrt{s}$, of 300 and 318 GeV. No evidence of lepton-flavor violation was found, and constraints were derived on leptoquarks (LQs) that could mediate such interactions. For LQ masses below $\sqrt{s}$, limits were set on $\lambda_{eq_1} \sqrt{\beta_{\ell q}}$, where $\lambda_{eq_1}$ is the coupling of the LQ to an electron and a first-generation quark $q_1$, and $\beta_{\ell q}$ is the branching ratio of the LQ to the final-state lepton $\ell$ ($\mu$ or $\tau$) and a quark $q$. For LQ masses much larger than $\sqrt{s}$, limits were set on the four-fermion interaction term $\lambda_{e q_\alpha} \lambda_{\ell q_\beta} / M_{\mathrm{LQ}}^2$ for LQs that couple to an electron and a quark $q_\alpha$ and to a lepton $\ell$ and a quark $q_\beta$, where $\alpha$ and $\beta$ are quark generation indices. Some of the limits are also applicable to lepton-flavor-violating processes mediated by squarks in $R$-Parity-violating supersymmetric models. In some cases, especially when a higher-generation quark is involved and for the process $e p\to \tau X$, the ZEUS limits are the most stringent to date.Comment: 37 pages, 10 figures, Accepted by EPJC. References and 1 figure (Fig. 6) adde

Multijet production in neutral current deep inelastic scattering at HERA and determination of alpha_s

Multijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities 10 < Q2 < 5000 GeV2. The data were taken at the ep collider HERA with centre-of-mass energy sqrt(s) = 318 GeV using the ZEUS detector and correspond to an integrated luminosity of 82.2 pb-1. Jets were identified in the Breit frame using the k_T cluster algorithm in the longitudinally invariant inclusive mode. Measurements of differential dijet and trijet cross sections are presented as functions of jet transverse energy E_{T,B}{jet}, pseudorapidity eta_{LAB}{jet} and Q2 with E_{T,B}{jet} > 5 GeV and -1 < eta_{LAB}{jet} < 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant alpha_s(M_Z), determined from the ratio of the trijet to dijet cross sections, is alpha_s(M_Z) = 0.1179 pm 0.0013(stat.) {+0.0028}_{-0.0046}(exp.) {+0.0064}_{-0.0046}(th.)Comment: 22 pages, 5 figure

Measurement of (anti)deuteron and (anti)proton production in DIS at HERA

The first observation of (anti)deuterons in deep inelastic scattering at HERA has been made with the ZEUS detector at a centre-of-mass energy of 300--318 GeV using an integrated luminosity of 120 pb-1. The measurement was performed in the central rapidity region for transverse momentum per unit of mass in the range 0.3<p_T/M<0.7. The particle rates have been extracted and interpreted in terms of the coalescence model. The (anti)deuteron production yield is smaller than the (anti)proton yield by approximately three orders of magnitude, consistent with the world measurements.Comment: 26 pages, 9 figures, 5 tables, submitted to Nucl. Phys.

Photoproduction of D∗±D^{*\pm} mesons associated with a leading neutron

The photoproduction of $D^{*\pm} (2010)$ mesons associated with a leading neutron has been observed with the ZEUS detector in $ep$ collisions at HERA using an integrated luminosity of 80 pb$^{-1}$. The neutron carries a large fraction, {$x_L>0.2$}, of the incoming proton beam energy and is detected at very small production angles, {$\theta_n<0.8$ mrad}, an indication of peripheral scattering. The $D^*$ meson is centrally produced with pseudorapidity {$|\eta| 1.9$ GeV}, which is large compared to the average transverse momentum of the neutron of 0.22 GeV. The ratio of neutron-tagged to inclusive $D^*$ production is $8.85\pm 0.93({\rm stat.})^{+0.48}_{-0.61}({\rm syst.})\%$ in the photon-proton center-of-mass energy range {$130 <W<280$ GeV}. The data suggest that the presence of a hard scale enhances the fraction of events with a leading neutron in the final state.Comment: 28 pages, 4 figures, 2 table

Measurement of the open-charm contribution to the diffractive proton structure function

Production of D*+/-(2010) mesons in diffractive deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 82 pb^{-1}. Diffractive events were identified by the presence of a large rapidity gap in the final state. Differential cross sections have been measured in the kinematic region 1.5 < Q^2 < 200 GeV^2, 0.02 < y < 0.7, x_{IP} < 0.035, beta 1.5 GeV and |\eta(D*+/-)| < 1.5. The measured cross sections are compared to theoretical predictions. The results are presented in terms of the open-charm contribution to the diffractive proton structure function. The data demonstrate a strong sensitivity to the diffractive parton densities.Comment: 35 pages, 11 figures, 6 table

Measurement of beauty production in deep inelastic scattering at HERA

The beauty production cross section for deep inelastic scattering events with at least one hard jet in the Breit frame together with a muon has been measured, for photon virtualities Q^2 > 2 GeV^2, with the ZEUS detector at HERA using integrated luminosity of 72 pb^-1. The total visible cross section is sigma_b-bbar (ep -> e jet mu X) = 40.9 +- 5.7 (stat.) +6.0 -4.4 (syst.) pb. The next-to-leading order QCD prediction lies about 2.5 standard deviations below the data. The differential cross sections are in general consistent with the NLO QCD predictions; however at low values of Q^2, Bjorken x, and muon transverse momentum, and high values of jet transverse energy and muon pseudorapidity, the prediction is about two standard deviations below the data.Comment: 18 pages, 4 figure