Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use dynamical network approach to evaluate the collective financial failure---systemic risk---quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided on sub-periods, where within each sub-period banks may contiguously fail due to links to either (i) assets or (ii) other banks, controlled by two parameters, probability of internal failure $p$ and threshold $T_h$ ("solvency" parameter). The systemic risk non-linearly increases with $p$ and decreases with average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller $T_h$), the smaller the systemic risk---for some $T_h$ values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic (ii) controlled by probability $p_2$---a condition for the bank to be solvent (active) is stochastic---the systemic risk decreases with decreasing $p_2$. We analyse asset allocation for the U.S. banks.Comment: 7 pages, 7 figure

Neutron diffraction investigation of the H-T phase diagram above the longitudinal incommensurate phase of BaCo2V2O8

The quasi-one-dimensional antiferromagnetic Ising-like compound BaCo2V2O8 has been shown to be describable by the Tomonaga-Luttinger liquid theory in its gapless phase induced by a magnetic field applied along the Ising axis. Above 3.9 T, this leads to an exotic field-induced low-temperature magnetic order, made of a longitudinal incommensurate spin-density wave, stabilized by weak interchain interactions. By single-crystal neutron diffraction we explore the destabilization of this phase at a higher magnetic field. We evidence a transition at around 8.5 T towards a more conventional magnetic structure with antiferromagnetic components in the plane perpendicular to the magnetic field. The phase diagram boundaries and the nature of this second field-induced phase are discussed with respect to previous results obtained by means of nuclear magnetic resonance and electron spin resonance, and in the framework of the simple model based on the Tomonaga-Luttinger liquid theory, which obviously has to be refined in this complex system.Comment: 7 pages, 5 figure

Bankruptcy risk model and empirical tests

We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor-the debt-to-asset ratio R-in order to study the stability of the Zipf distribution of R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayes's theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees-although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers.Comment: 8 pages, 8 figure

Field Induced Staggered Magnetization and Magnetic Ordering in Cu2(C5H12N2)2Cl4Cu_2 (C_5 H_{12} N_2)_2 Cl_4

We present a $^2$D NMR investigation of the gapped spin-1/2 compound $Cu_2 (C_5 H_{12} N_2)_2 Cl_4$. Our measurements reveal the presence of a magnetic field induced transverse staggered magnetization (TSM) which persists well below and above the field-induced 3D long-range magnetically ordered (FIMO) phase. The symmetry of this TSM is different from that of the TSM induced by the order parameter of the FIMO phase. Its origin, field dependence and symmetry can be explained by an intra-dimer Dzyaloshinskii-Moriya interaction, as shown by DMRG calculations on a spin-1/2 ladder. This leads us to predict that the transition into the FIMO phase is not in the BEC universality class.Comment: 4 page

Magnetic Field Effects on Quasiparticles in Strongly Correlated Local Systems

We show that quasiparticles in a magnetic field of arbitrary strength $H$ can be described by field dependent parameters. We illustrate this approach in the case of an Anderson impurity model and use the numerical renormalization group (NRG) to calculate the renormalized parameters for the levels with spin $\sigma$, $\tilde\epsilon_{\mathrm{d},\sigma}(H)$, resonance width $\tilde\Delta(H)$ and the effective local quasiparticle interaction $\tilde U(H)$. In the Kondo or strong correlation limit of the model the progressive de-renormalization of the quasiparticles can be followed as the magnetic field is increased. The low temperature behaviour, including the conductivity, in arbitrary magnetic field can be calculated in terms of the field dependent parameters using the renormalized perturbation expansion. Using the NRG the field dependence of the spectral density on higher scales is also calculated.Comment: 15 pages, 17 figure

Effect of the Kondo correlation on thermopower in a Quantum Dot

In this paper we study the thermopower of a quantum dot connected to two leads in the presence of Kondo correlation by employing a modified second-order perturbation scheme at nonequilibrium. A simple scheme, Ng's ansatz [Phys. Rev. Lett. {\bf 76}, 487 (1996)], is adopted to calculate nonequilibrium distribution Green's function and its validity is further checked with regard to the Onsager relation. Numerical results demonstrate that the sign of the thermopower can be changed by tuning the energy level of the quantum dot, leading to a oscillatory behavior with a suppressed magnitude due to the Kondo effect. We also calculate the thermal conductance of the system, and find that the Wiedemann-Franz law is obeyed at low temperature but violated with increasing temperature, corresponding to emerging and quenching of the Kondo effect.Comment: 6 pages, 4 figures; accepted for publication in J Phys.: Condensed Matte

Common scaling behavior in finance and macroeconomics

In order to test whether scaling exists in finance at the world level, we test whether the average growth rates and volatility of market capitalization (MC) depend on the level of MC. We analyze the MC for 54 worldwide stock indices and 48 worldwide bond indices. We find that (i) the average growth rate $\langle$ r $\rangle$ of the MC and (ii) the standard deviation $\sigma(r)$ of growth rates r decrease both with MC as power laws, with exponents $\alpha_w$ = 0.28 ± 0.09 and $\beta_w$ = 0.12 ± 0.04. We define a stochastic process in order to model the scaling results we find for worldwide stock and bond indices. We establish a power-law relationship between the MC of a country's financial market and the gross domestic product (GDP) of the same countr

Dynamic susceptibilities of the single impurity Anderson model within an enhanced non-crossing approximation

The single impurity Anderson model (SIAM) is studied within an enhanced non-crossing approximation (ENCA). This method is extended to the calculation of susceptibilities and thoroughly tested, also in order to prepare applications as a building block for the calculation of susceptibilities and phase transitions in correlated lattice systems. A wide range of model parameters, such as impurity occupancy, temperature, local Coulomb repulsion and hybridization strength, are studied. Results for the spin and charge susceptibilities are presented. By comparing the static quantities to exact Bethe ansatz results, it is shown that the description of the magnetic excitations of the impurity within the ENCA is excellent, even in situations with large valence fluctuations or vanishing Coulomb repulsion. The description of the charge susceptibility is quite accurate in situations where the singly occupied ionic configuration is the unperturbed ground state; however, it seems to overestimate charge fluctuations in the asymmetric model at too low temperatures. The dynamic spin excitation spectra is dominated by the Kondo-screening of the impurity spin through the conduction band, i.e. the formation of the local Kondo-singlet. A finite local Coulomb interaction U leads to a drastic reduction of the charge response via processes involving the doubly occupied impurity state. In the asymmetric model, the charge susceptibility is enhanced for excitation energies smaller than the Kondo scale T_K due to the influence of valence fluctuations.Comment: 16 pages, 13 figure