Adequate Capital and Stress Testing for Operational Risks

We describe how the notion of sequential correlations naturally leads to the quantification of operational risk. Our main point is that functional dependencies between mutually supportive processes give rise to non-trivial temporal correlations, which can lead to the occurrence of collective risk events in the form of bursts and avalanches of process failures, and crashes of process networks. We show how the adequate capital for operational risk can be calculated via a stochastic dynamics defined on a topological network of interacting processes. One of the main virtues of the present model is the suitability for capital allocation and stress testing of operational risks

Intermittency in an interacting generalization of the geometric Brownian motion model

We propose a minimal interacting generalization of the geometric Brownian motion model, which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons. For sufficiently strong interactions, such systems may have many meta-stable states. Transitions between meta-stable states are associated with macroscopic reorganizations of the system, which can be triggered by random external forcing. Such a system will exhibit intermittent dynamics within a large part of its parameter space. We propose market dynamics as a possible application of this model, in which case random external forcing would correspond to the arrival of important information. The emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non-price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences. PACS numbers: 02.50.−r, 05.40.−a, 89.65.Gh, 89.75.Da 1

К вопросу о новых философских основаниях гуманизма

Представлено новое направление философских поисков для определения понятия "гуманизм". Новые философские основания гуманизма позволят выработать обновленное видение отношений человека, общества и природы

Functional Correlation Approach to Operational Risk in Banking Organizations

A Value-at-Risk based model is proposed to compute the adequate equity capital necessary to cover potential losses due to operational risks, such as human and system process failures, in banking organizations. Exploring the analogy to a lattice gas model from physics, correlations between sequential failures are modeled by as functionally defined, heterogeneous couplings between mutually supportive processes. In contrast to traditional risk models for market and credit risk, where correlations are described by the covariance of Gaussian processes, the dynamics of the model shows collective phenomena such as bursts and avalanches of process failures.Comment: 12 pages, 7 figures, uses RevTeX 4.0, submitted to Phys. Rev.

Tunneling dynamics of side chains and defects in proteins, polymer glasses, and OH-doped network glasses

Simulations on a Lennard-Jones computer glass are performed to study effects arising from defects in glasses at low temperatures. The numerical analysis reveals that already a low concentration of defects may dramatically change the low temperature properties by giving rise to extrinsic double-well potentials (DWP's). The main characteristics of these extrinsic DWP's are (i) high barrier heights, (ii) high probability that a defect is indeed connected with an extrinsic DWP, (iii) highly localized dynamics around this defect, and (iv) smaller deformation potential coupling to phonons. Designing an extension of the Standard Tunneling Model (STM) which parametrizes this picture and comparing with ultrasound experiments on the wet network glass $a$-B$_2$O$_3$ shows that effects of OH-impurities are accurately accounted for. This model is then applied to organic polymer glasses and proteins. It is suggested that side groups may act similarly like doped impurities inasmuch as extrinsic DWP's are induced, which possess a distribution of barriers peaked around a high barrier height. This compares with the structurlessly distributed barrier heights of the intrinsic DWP's, which are associated with the backbone dynamics. It is shown that this picture is consistent with elastic measurements on polymers, and can explain anomalous nonlogarithmic line broadening recently observed in hole burning experiments in PMMA.Comment: 34 pages, Revtex, 9 eps-figures, accepted for publication in J. Chem. Phy

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques