Admissible strategies in semimartingale portfolio selection

The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps [HK79]. In the context of optimal portfolio selection with expected utility preferences this question has been the focus of considerable attention over the last twenty years. We propose a novel notion of admissibility that has many pleasant features { admissibility is characterized purely under the objective measure P; each admissible strategy can be approximated by simple strategies using finite number of trading dates; the wealth of any admissible strategy is a supermartingale under all pricing measures; local boundedness of the price process is not required; neither strict monotonicity, strict concavity nor differentiability of the utility function are necessary; the definition encompasses both the classical mean-variance preferences and the monotone expected utility. For utility functions finite on R, our class represents a minimal set containing simple strategies which also contains the optimizer, under conditions that are milder than the celebrated reasonable asymptotic elasticity condition on the utility function

Unambiguous determination of the g-factor for holes in bismuth at high B/T

Magnetotransport has been investigated in high purity bismuth crystals in static magnetic fields as high as 20 T and temperatures as low as 25 mK. This high B/T ratio permits observation of pronounced Shubnikov-de Haas oscillations over a wide field range and up to fields where most of the carriers are in the lowest Landau level. For transport currents in the bisectrix or binary directions and field in the perpendicular trigonal direction, we have observed doublet splittings centered on each Shubnikov-de Haas oscillation. These splittings exhibit a quadratic dependence on field and disappear before the last oscillation. Our observations allow us to conclude unambiguously that already when the Landau level index is as high as 2 the carriers are fully polarized and that the g-factor for holes with the field in the trigonal direction is 35.3(4).Comment: 4 pages, 3 figure

Unitary and analytic model of nucleon EM structure, the puzzle with JLab proton polarization data and new insight into proton charge distribution

The Unitary and analytic model of nucleon electromagnetic structure, describing all existing nucleon form factor data, is briefly reviewed. Then in the framework of this model the problem of inconsistency of older proton electric form factor data in space-like region (obtained from $e^{-}p$ process by the Rosenbluth technique) with recent Jefferson Lab data on the ratio $G_{Ep}(t)/G_{Mp}(t)$ (measured in precise polarization $\overrightarrow{e}^{-}p\to e^{-}\overrightarrow{p}$ experiment) is suggested to be solved in favour of the latter data which, however, unlike older data cause an existence of the form factor zero, i.e. a difraction minimum in $|G_{Ep}(t)|$ around $t=-Q^{2}=-13$GeV$^{2}$. The new behaviour of $G_{Ep}(t)$ with the zero gives modified proton charge distribution with enlarged value of the mean square charge radius.Comment: 9 pages, 11 eps figures. Talk presented at the workshop on Lepton Scattering and the Structure of Hadrons and Nuclei, Erice (Italy), September 200

Magnetic-field-induced Luttinger liquid

It is shown that a strong magnetic field applied to a bulk metal induces a Luttinger-liquid phase. This phase is characterized by the zero-bias anomaly in tunneling: the tunneling conductance scales as a power-law of voltage or temperature. The tunneling exponent increases with the magnetic field as BlnB. The zero-bias anomaly is most pronounced for tunneling with the field applied perpendicular to the plane of the tunneling junction.Comment: a reference added, minor typos correcte

Many-Body Effects on Tunneling of Electrons in Magnetic-Field-Induced Quasi One-Dimensional Electron Systems in Semiconductor Nanowhiskers

Effects of the electron-electron interaction on tunneling in a semiconductor nanowhisker are studied in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. In bulk states, the temperature dependence of the transmission probability is qualitatively similar to that of a one-dimensional electron system. We investigate contributions of edge states on transmission probability in bulk states. Those contributions can be neglected within our approximation which takes into account only most divergent terms at low temperatures.Comment: 9 pages, 6 figure

Nucleation of superconducting pairing states at mesoscopic scales at zero temperature

We find the spin polarized disordered Fermi liquids are unstable to the nucleation of superconducting pairing states at mesoscopic scales even when magnetic fields which polarize the spins are substantially higher than the critical one. We study the probability of finding superconducting pairing states at mesoscopic scales in this limit. We find that the distribution function depends only on the film conductance. The typical length scale at which pairing takes place is universal, and decreases when the magnetic field is increased. The number density of these states determines the strength of the random exchange interactions between mesoscopic pairing states.Comment: 11 pages, no figure