A Diffusion Approximation for the Riskless Profit Under Selling of Discrete Time Call Options. Non-identically Distributed Jumps

A discrete time model of financial markets is considered. It is assumed that the relative jumps of the risky security price are independent non-identically distributed random variables. In the focus of attention is the expected non-risky profit of the investor that arises when the jumps of the stock price are bounded while the investor follows the upper hedge. The considered discrete time model is approximated by a continuous time model that generalizes the classical geometrical Brownian motion.Asymptotic uniformity, Local limit theorem, Volatility

A Diffusion Approximation to the Markov Chains Model of the Financial Market and the Expected Riskless Profit Under Selling of Call and Put Options

A discrete time model of financial markets is considered. It is assumed that the stock price evolution is described by a homogeneous Markov chain. In the focus of attention is the expected value of the guaranteed profit of the investor that arises when the jumps of the stock price are bounded. The suggested diffusion approximation for the Markov chain allows establishing a convenient approximate formula for the studied characteristic.Ergodic and irreducible Markov chains, Stationary distribution, Local limit theorem, Upper hedge, Upper rational price

Phase diagram as a function of temperature and magnetic field for magnetic semiconductors

Using an extension of the Nagaev model of phase separation (E.L. Nagaev, and A.I. Podel'shchikov, Sov. Phys. JETP, 71 (1990) 1108), we calculate the phase diagram for degenerate antiferromagnetic semiconductors in the T-H plane for different current carrier densities. Both, wide-band semiconductors and 'double-exchange' materials, are investigated.Comment: 5 pages, 6 figures, RevTex, Accepted for publication in PR

The phase-separated states in antiferromagnetic semiconductors with polarizable lattice

The possibility of the slab or stripe phase separation (alternating ferromagnetic highly- conductive and insulating antiferromagnetic layers) is proved for isotropic degenerate antiferromagnetic semiconductors. This type of phase separation competes with the droplet phase separation (ferromagnetic droplets in the antiferromagnetic host or vice versa). The interaction of electrons with optical phonons alone cannot cause phase-separated state with alternating highly-conductive and insulating regions but it stabilizes the magnetic phase separation. The magnetostriction deformation of the lattice in the phase-separated state is investigated.Comment: 17 Pages, 1 EPS Figur

Frequency-Dependent Shot Noise as a Probe of Electron-Electron Interaction in Mesoscopic Diffusive Contacts

The frequency-dependent shot noise in long and narrow mesoscopic diffusive contacts is numerically calculated. The case of arbitrarily strong electron-electron scattering and zero temperature of electrodes is considered. For all voltages, the noise increases with frequency and tends to finite values. These limiting values are larger than the Poissonian noise and increase nearly as voltage to power 4/3. This allows one to experimentally determine the parameters of electron-electron interaction.Comment: 3 pages, RevTeX, 3 eps figure

Semiclassical theory of shot noise in disordered SN contacts

We present a semiclassical theory of shot noise in diffusive superconductor - normal metal contacts. At subgap voltages, we reproduce the doubling of shot noise with respect to conventional normal-metal contacts, which is interpreted in terms of an energy balance of electrons. Above the gap, the voltage dependence of the noise crosses over to the standard one with a voltage-independent excess noise. The semiclassical description of noise leads to correlations between currents at different electrodes of multiterminal SN contacts which are always of fermionic type, i.e. negative. Using a quantum extension of the Boltzmann - Langevin method, we reproduce the peculiarity of noise at the Josephson frequency and obtain an analytical frequency dependence of noise at above-gap voltages.Comment: 4 pages RevTeX, 1 eps figur

Inhomogeneous Phases in a Double-Exchange Magnet with Long Range Coulomb Interactions

We consider a model with competing double-exchange (ferromagnetic) and super-exchange (anti-ferromagnetic) interactions in the regime where phase separation takes place. The presence of a long range Coulomb interaction frustrates a macroscopic phase separation, and favors microscopically inhomogeneous configurations. We use the variational Hartree-Fock approach, in conjunction with Monte-Carlo simulations to study the geometry of such configurations in a two-dimensional system. We find that an array of diamond shaped ferromagnetic droplets is the preferred configuration at low electronic densities, while alternating ferromagnetic and anti-ferromagnetic diagonal stripes emerge at higher densities. These findings are expected to be relevant for thin films of colossal magneto-resistive manganates.Comment: 15 pages, 9 figures. Journal Ref. added, errors correcte

Nanoscale phase separation in manganites

We study the possibility of nanoscale phase separation in manganites in the framework of the double exchange model. The homogeneous canted state of this model is proved to be unstable toward the formation of small ferromagnetic droplets inside an antiferromagnetic insulating matrix. For the ferromagnetic polaronic state we analyze the quantum effects related to the tails of electronic wave function and a possibility of electron hopping in the antiferromagnetic background. We find that these effects lead to the formation of the threshold for the polaronic state.Comment: 10 pages, 2 figures, invited talk on the workshop on Strongly Correlated Electrons in New Materials (SCENM02), Loughborough (UK). submitted to Journal of Physics A: Mathematical and Genera