Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting

The dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering including the effects of nuclear dynamics by extending the common many-body Green's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and the nuclear motion of the target molecule on the same footing whereby the dynamical optical potential rigorously accounts for the complex many-body nature of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximation to the dynamical optical potential even when projectile and nuclear motion are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the influences of the nuclear dynamics on the optical potential to become relevant. For these cases, a systematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields non-local operators with respect to the nuclear coordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.

The unidentified TeV source (TeVJ2032+4130) and surrounding field: Final HEGRA IACT-System results

The unidentified TeV source in Cygnus is now confirmed by follow-up observations from 2002 with the HEGRA stereoscopic system of Cherenkov Telescopes. Using all data (1999 to 2002) we confirm this new source as steady in flux over the four years of data taking, extended with radius 6.2 arcmin (+-1.2 arcmin (stat) +-0.9 arcmin (sys)) and exhibiting a hard spectrum with photon index -1.9. It is located in the direction of the dense OB stellar association, Cygnus OB2. Its integral flux above energies E>1 TeV amounts to \~5% of the Crab assuming a Gaussian profile for the intrinsic source morphology. There is no obvious counterpart at radio, optical nor X-ray energies, leaving TeVJ2032+4130 presently unidentified. Observational parameters of this source are updated here and some astrophysical discussion is provided. Also included are upper limits for a number of other interesting sources in the FoV, including the famous microquasar Cygnus X-3.Comment: 7 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic

The Energy Spectrum of TeV Gamma-Rays from the Crab Nebula as measured by the HEGRA system of imaging air Cherenkov telescopes

The Crab Nebula has been observed by the HEGRA (High-Energy Gamma-Ray Astronomy) stereoscopic system of imaging air Cherenkov telescopes (IACTs) for a total of about 200 hrs during two observational campaigns: from September 1997 to March 1998 and from August 1998 to April 1999. The recent detailed studies of system performance give an energy threshold and an energy resolution for gamma-rays of 500 GeV and ~ 18%, respectively. The Crab energy spectrum was measured with the HEGRA IACT system in a very broad energy range up to 20 TeV, using observations at zenith angles up to 65 degrees. The Crab data can be fitted in the energy range from 1 to 20 TeV by a simple power-law, which yields dJg/dE = (2.79+/-0.02 +/- 0.5) 10^{-7} E^{-2.59 +/- 0.03 +/- 0.05}, ph m^{-2} s^{-1} TeV^{-1} The Crab Nebula energy spectrum, as measured with the HEGRA IACT system, agrees within 15% in the absolute scale and within 0.1 units in the power law index with the latest measurements by the Whipple, CANGAROO and CAT groups, consistent within the statistical and systematic errors quoted by the experiments. The pure power-law spectrum of TeV gamma-rays from the Crab Nebula constrains the physics parameters of the nebula environment as well as the models of photon emission.Comment: to appear in ApJ, 29 pages, 6 figure

Simultaneous X-Ray and TeV Gamma-Ray Observations of the TeV Blazar Markarian 421 during February and May 2000

In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 (Mrk 421) at X-ray and TeV Gamma-ray energies with the Rossi X-Ray Timing Explorer (RXTE) and the stereoscopic Cherenkov Telescope system of the HEGRA (High Energy Gamma Ray Astronomy) experiment, respectively. The source was monitored from February 2nd to February 16th and from May 3rd to May 8th, 2000. We discuss in detail the temporal and spectral properties of the source. Remarkably, the TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale. We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton (SSC) model. The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher. The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones.Comment: Accepted for Publication in ApJ, 21 Pages, 5 Figure

Optical study of orbital excitations in transition-metal oxides

The orbital excitations of a series of transition-metal compounds are studied by means of optical spectroscopy. Our aim was to identify signatures of collective orbital excitations by comparison with experimental and theoretical results for predominantly local crystal-field excitations. To this end, we have studied TiOCl, RTiO3 (R=La, Sm, Y), LaMnO3, Y2BaNiO5, CaCu2O3, and K4Cu4OCl10, ranging from early to late transition-metal ions, from t_2g to e_g systems, and including systems in which the exchange coupling is predominantly three-dimensional, one-dimensional or zero-dimensional. With the exception of LaMnO3, we find orbital excitations in all compounds. We discuss the competition between orbital fluctuations (for dominant exchange coupling) and crystal-field splitting (for dominant coupling to the lattice). Comparison of our experimental results with configuration-interaction cluster calculations in general yield good agreement, demonstrating that the coupling to the lattice is important for a quantitative description of the orbital excitations in these compounds. However, detailed theoretical predictions for the contribution of collective orbital modes to the optical conductivity (e.g., the line shape or the polarization dependence) are required to decide on a possible contribution of orbital fluctuations at low energies, in particular in case of the orbital excitations at about 0.25 eV in RTiO3. Further calculations are called for which take into account the exchange interactions between the orbitals and the coupling to the lattice on an equal footing.Comment: published version, discussion of TiOCl extended to low T, improved calculation of orbital excitation energies in TiOCl, figure 16 improved, references updated, 33 pages, 20 figure