Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions

We study the general model of self-financing trading strategies in illiquid markets introduced by Schoenbucher and Wilmott, 2000. A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(alpha). This function is deep connected to an utility function. We describe the Lie symmetry algebra of this PDE and provide a complete set of reductions of the PDE to ordinary differential equations (ODEs). In addition we are able to describe all types of functions g(alpha) for which the PDE admits an extended Lie group. Two of three special type functions lead to models introduced before by different authors, one is new. We clarify the connection between these three special models and the general model for trading strategies in illiquid markets. We study with the Lie group analysis the new special case of the PDE describing the self-financing strategies. In both, the general model and the new special model, we provide the optimal systems of subalgebras and study the complete set of reductions of the PDEs to different ODEs. In all cases we are able to provide explicit solutions to the new special model. In one of the cases the solutions describe power derivative products.Comment: 17 pages, 3 figure

Present and Future Experiments in Non-equilibrium Reactor Antineutrino Energy Spectrum

Considerable efforts that have been undertaken in the recent years in low energy antineutrino experiments require further systematic investigations in line of reactor antineutrino spectroscopy as a metrological basis of these experiments. We consider some effects associated with the non-equilibrium of reactor antineutrino radiation and residual antineutrino emission from spent reactor fuel in contemporary antineutrino experiments.Comment: 7 pages, 5 figures; Talk presented at International Conference NANP-2005, Dubna, Russia, Jun.-2005; Submitted to Phys. Atom. Nuc

Two Detector Reactor Neutrino Oscillation Experiment Kr2Det at Krasnoyarsk. Status Report

We consider status of the Kr2Det project aimed at sensitive searches for neutrino oscillations in the atmospheric neutrino mass parameter region around Dm2 ~ 3x10-3 eV2and at obtaining new information on the electron neutrino mass structure (Ue3).Comment: 4 pages in pdf file. Talk presented at NANP-2001 International Conference in Dubna, Russia, June 200

The Kr2Det project: Search for mass-3 state contribution |U_{e3}|^2 to the electron neutrino using a one reactor - two detector oscillation experiment at Krasnoyarsk underground site

The main physical goal of the project is to search with reactor antineutrinos for small mixing angle oscillations in the atmospheric mass parameter region around {\Delta}m^{2}_{atm} ~ 2.5 10^{-3} eV^2 in order to find the element U_{e3} of the neutrino mixing matrix or to set a new more stringent constraint (U_{e3} is the contribution of mass-3 state to the electron neutrino flavor state). To achieve this we propose a "one reactor - two detector" experiment: two identical antineutrino spectrometers with $\sim$50 ton liquid scintillator targets located at ~100 m and ~1000 m from the Krasnoyarsk underground reactor (~600 mwe). In no-oscillation case ratio of measured positron spectra of the \bar{{\nu}_e} + p \to e^{+} + n reaction is energy independent. Deviation from a constant value of this ratio is the oscillation signature. In this scheme results do not depend on the exact knowledge of the reactor power, nu_e spectra, burn up effects, target volumes and, which is important, the backgrounds can periodically be measured during reactor OFF periods. In this letter we present the Krasnoyarsk reactor site, give a schematic description of the detectors, calculate the neutrino detection rates and estimate the backgrounds. We also outline the detector monitoring and calibration procedures, which are of a key importance. We hope that systematic uncertainties will not accede 0.5% and the sensitivity U^{2}_{e3} ~4 10^{-3} (at {\Delta}m^{2} = 2.5 10^{-3} eV^2) can be achieved.Comment: Latex 2e, 9 pages and 5 ps figure

Neutrino Geophysics at Baksan I: Possible Detection of Georeactor Antineutrinos

J.M. Herndon in 90-s proposed a natural nuclear fission georeactor at the center of the Earth with a power output of 3-10 TW as an energy source to sustain the Earth magnetic field. R.S. Raghavan in 2002 y. pointed out that under certain condition antineutrinos generated in georeactor can be detected using massive scintillation detectors. We consider the underground Baksan Neutrino Observatory (4800 m.w.e.) as a possible site for developments in Geoneutrino physics. Here the intrinsic background level of less than one event/year in a liquid scintillation ~1000 target ton detector can be achieved and the main source of background is the antineutrino flux from power reactors. We find that this flux is ~10 times lower than at KamLAND detector site and two times lower than at Gran Sasso laboratory and thus at Baksan the georeactor hypothesis can be conclusively tested. We also discuss possible search for composition of georector burning nuclear fuel by analysis of the antineutrino energy spectrum.Comment: 7 pages in LaTeX, 3 PS figures, Submitted to Physics of Atomic Nucle

Determining Neutrino Mass Hierarchy by Precision Measurements in Electron and Muon Neutrino Disappearance Experiments

Recently a new method for determining the neutrino mass hierarchy by comparing the effective values of the atmospheric \Delta m^2 measured in the electron neutrino disappearance channel, \Delta m^2(ee), with the one measured in the muon neutrino disappearance channel, \Delta m^2(\mu \mu), was proposed. If \Delta m^2(ee) is larger (smaller) than \Delta m^2(\mu \mu) the hierarchy is of the normal (inverted) type. We re-examine this proposition in the light of two very high precision measurements: \Delta m^2(\mu \mu) that may be accomplished by the phase II of the Tokai-to-Kamioka (T2K) experiment, for example, and \Delta m^2(ee) that can be envisaged using the novel Mossbauer enhanced resonant \bar\nu_e absorption technique. Under optimistic assumptions for the systematic uncertainties of both measurements, we estimate the parameter region of (\theta_13, \delta) in which the mass hierarchy can be determined. If \theta_13 is relatively large, sin^2 2\theta_13 \gsim 0.05, and both of \Delta m^2(ee) and \Delta m^2(\mu \mu) can be measured with the precision of \sim 0.5 % it is possible to determine the neutrino mass hierarchy at > 95% CL for 0.3 \pi \lsim \delta \lsim 1.7 \pi for the current best fit values of all the other oscillation parameters.Comment: 12 pages, 6 postscript figure

Nuclear Propelled Vessels and Neutrino Oscillation Experiments

We study the effect of naval nuclear reactors on the study of neutrino oscillations. We find that the presence of naval reactors at unknown locations and times may limit the accuracy of future very long baseline reactor-based neutrino oscillation experiments. At the same time we argue that a nuclear powered surface ship such as a large Russian ice-breaker may provide an ideal source for precision experiments. While the relatively low reactor power would in this case require a larger detector, the source could be conveniently located at essentially any distance from a detector built at an underground location near a shore in a region of the world far away from other nuclear installations. The variable baseline would allow for a precise measurement of backgrounds and greatly reduced systematics from reactor flux and detector efficiency. In addition, once the oscillation measurement is completed, the detector could perform geological neutrino and astrophysical measurements with minimal reactor background.Comment: 4 pages, 2 figure

Weak and Magnetic Inelastic Scattering of Antineutrinos on Atomic Electrons

Neutrino scattering on electrons is considered as a tool for laboratory searches of the neutrino magnetic moment. We study inelastic $\bar\nu_ee^-$-scattering on electrons bound in the germanium (Z=32) and iodine (Z=53) atoms for antineutrinos generated in a nuclear reactor core and also in the $^{90}$Sr-$^{90}$Y and $^{147}$Pm artificial sources. Using the relativistic Hartree-Fock-Dirac model, we calculate both the magnetic and weak scattering cross sections for the recoil electron energy range of 1 to 100 keV where a higher sensitivity to the neutrino magnetic moment could be achieved. Particular attention is paid to the approximate procedure which allows us to take into account the effects of atomic binding on the inelastic scattering spectra in a simple way.Comment: 7 pages in LaTeX, 10 figures in P