News and price returns from threshold behaviour and vice-versa: exact solution of a simple agent-based market model

Starting from an exact relationship between news, threshold and price return distributions in the stationary state, I discuss the ability of the Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under normal conditions, this model is not able to transform Gaussian news into fat-tailed price returns. When the variance of the news so small that only the players with zero threshold can possibly react to news, this model produces Levy-distributed price returns with a -1 exponent. In the special case of super-linear price impact functions, fat-tailed returns are obtained from well-behaved news.Comment: 4 pages, 3 figures. This is quite possibly the final version. To appear in J. Phys

Risk margin for a non-life insurance run-off

For solvency purposes insurance companies need to calculate so-called best-estimate reserves for outstanding loss liability cash flows and a corresponding risk margin for non-hedgeable insurance-technical risks in these cash flows. In actuarial practice, the calculation of the risk margin is often not based on a sound model but various simplified methods are used. In the present paper we properly define these notions and we introduce insurance-technical probability distortions. We describe how the latter can be used to calculate a risk margin for non-life insurance run-off liabilities in a mathematically consistent way

Theoretical Sensitivity Analysis for Quantitative Operational Risk Management

We study the asymptotic behavior of the difference between the values at risk VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application in sensitivity analysis of quantitative operational risk management within the framework of the advanced measurement approach of Basel II (and III). Here L describes the loss amount of the present risk profile and S describes the loss amount caused by an additional loss factor. We obtain different types of results according to the relative magnitudes of the thicknesses of the tails of L and S. In particular, if the tail of S is sufficiently thinner than the tail of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the expectation (expected loss) of S.Comment: 21 pages, 1 figure, 4 tables, forthcoming in International Journal of Theoretical and Applied Finance (IJTAF

Bridging the ARCH model for finance and nonextensive entropy

Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterized by a time-dependent variance. It involves a memory parameter $b$ ($b=0$ corresponds to {\it no memory}), and the noise is currently chosen to be Gaussian. We assume here a generalized noise, namely $q_n$-Gaussian, characterized by an index $q_{n} \in {\cal R}$ ($q_{n}=1$ recovers the Gaussian case, and $q_n>1$ corresponds to tailed distributions). We then match the second and fourth momenta of the ARCH return distribution with those associated with the $q$-Gaussian distribution obtained through optimization of the entropy S_{q}=\frac{% 1-\sum_{i} {p_i}^q}{q-1}, basis of nonextensive statistical mechanics. The outcome is an {\it analytic} distribution for the returns, where an unique $q\ge q_n$ corresponds to each pair $(b,q_n)$ ($q=q_n$ if $b=0$). This distribution is compared with numerical results and appears to be remarkably precise. This system constitutes a simple, low-dimensional, dynamical mechanism which accommodates well within the current nonextensive framework.Comment: 4 pages, 5 figures.Figure 4 fixe

Self-Complementary Recognition of Supramolecular Urea - Aminotriazines in Solution and on Surfaces

The recognition of self-complementary quadruple urea–aminotriazine (UAT)-based hydrogen-bonded arrays was investigated in solution and at surfaces. For this purpose, an UAT-based donor–acceptor–donor–acceptor (DADA) array and complementary receptors were synthesized. Two-dimensional proton nuclear magnetic resonance (1H NMR) measurements in CDCl3 pointed at an intramolecular hydrogen-bond stabilization of the UAT, which promotes a planar molecular geometry and, thereby, results in a significant stabilization of the dimeric complex. The bond strength of the UAT dimers at surfaces was determined by atomic force microscopy-based single molecule force spectroscopy (AFM–SMFS) in hexadecane. The UAT receptor was immobilized on gold surfaces using an ultrathin layer of ethylene glycol terminated lipoic acid and isocyanate chemistry. The layers obtained and the reversible self-complementary recognition were thoroughly characterized with contact angle measurements, grazing angle Fourier transform infrared (FTIR) spectroscopy, X-ray photoelectron spectroscopy (XPS), and AFM. Loading rate-dependent SMFS measurements yielded a barrier width xβ and a bond lifetime at zero force toff(0) of 0.29 ± 0.02 nm and 100 ± 80 ms, respectively. The value of the corresponding off-rate constant koff suggests a substantially larger value of the dimerization constant compared to theoretical predictions, which is fully in line with the additional intramolecular hydrogen-bond stabilization detected in solution by 1H NMR spectroscopy

How Heavy Are the Tails of a Stationary HARCH(k) Process? A Study of the Moments

How Heavy Are the Tails of a Stationary HARCH(k) Process? A Study of the Moment

Density of near-extreme events

We provide a quantitative analysis of the phenomenon of crowding of near-extreme events by computing exactly the density of states (DOS) near the maximum of a set of independent and identically distributed random variables. We show that the mean DOS converges to three different limiting forms depending on whether the tail of the distribution of the random variables decays slower than, faster than, or as a pure exponential function. We argue that some of these results would remain valid even for certain {\em correlated} cases and verify it for power-law correlated stationary Gaussian sequences. Satisfactory agreement is found between the near-maximum crowding in the summer temperature reconstruction data of western Siberia and the theoretical prediction.Comment: 4 pages, 3 figures, revtex4. Minor corrections, references updated. This is slightly extended version of the Published one (Phys. Rev. Lett.

Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

Uievliegbestrijding door middel van zaadcoating bij prei

Veldproeven werden aangelegd om de bescherming tegen de made van de uievlieg te onderzoeken door het zaad te coaten met insekticiden. Verschillende doseringen van insekticiden werden onderzocht op 3 verschillende locaties in het land met een hoge populatie van de uievlie

Extreme value distributions for weakly correlated fitnesses in block model

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.Comment: Expanded, added reference