Portfolio optimization in the case of an asset with a given liquidation time distribution

Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses in this case we need to develop new methods. One of the steps moving the theory towards practical needs is to take into account the time lag of the liquidation of an illiquid asset. This task became especially significant for the practitioners in the time of the global financial crises. Working in the Merton's optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. While a standard Black-Scholes market describes the liquid part of the investment the illiquid asset is sold at a random moment with prescribed liquidation time distribution. In the moment of liquidation it generates additional liquid wealth dependent on illiquid assets paper value. The investor has the logarithmic utility function as a limit case of a HARA-type utility. Different distributions of the liquidation time of the illiquid asset are under consideration - a classical exponential distribution and Weibull distribution that is more practically relevant. Under certain conditions we show the existence of the viscosity solution in both cases. Applying numerical methods we compare classical Merton's strategies and the optimal consumption-allocation strategies for portfolios with different liquidation-time distributions of an illiquid asset.Comment: 30 pages, 1 figur

Generalized Efimov effect in one dimension

We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.Comment: 5+3 pages, 3 figures, published versio

Anisotropic interaction of two-level systems with acoustic waves in disordered crystals

We apply the model introduced in Phys. Rev. B 75, 064202 (2007), cond-mat/0610469, to calculate the anisotropy effect in the interaction of two level systems with phonons in disordered crystals. We particularize our calculations to cubic crystals and compare them with the available experimental data to extract the parameters of the model. With these parameters we calculate the interaction of the dynamical defects in the disordered crystal with phonons (or sound waves) propagating along other crystalographic directions, providing in this way a method to investigate if the anisotropy comes from the two-level systems being preferably oriented in a certain direction or solely from the lattice anisotropy with the two-level systems being isotropically oriented.Comment: 10 page

Electron paramagnetic resonance study of Eu2+ centers in melt-grown CsBr single crystals

The structure of Eu2+ monomer centers in CsBr single crystals is investigated using electron paramagnetic resonance (EPR) spectroscopy. These centers are produced by heating the melt-grown crystals above 600 K in vacuum followed by a rapid quench to room temperature (RT) or 77 K. The angular dependence of their EPR spectrum demonstrates that these centers have cubic symmetry. At RT the EPR spectrum decays by aggregation of the Eu2+ ions. This strongly contrasts with the situation for CsBr:Eu needle image plates synthesized by physical vapor deposition, where the Eu2+-related EPR spectrum was observed to exhibit long-term stability at RT

Stability of the Ground State of a Harmonic Oscillator in a Monochromatic Wave

Classical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and interacting with two lasers fields with close frequencies. Analytically and numerically a stability of the ``classical ground state'' (CGS) -- the vicinity of the point ($x=0, p=0$) -- is analyzed. In the quantum case, the method for studying a stability of the quantum ground state (QGS) is suggested, based on the quasienergy representation. The dynamics depends on four parameters: the detuning from the resonance, $\delta=\ell-\Omega/\omega$, where $\Omega$ and $\omega$ are, respectively, the wave and the oscillator's frequencies; the positive integer (resonance) number, $\ell$; the dimensionless Planck constant, $h$, and the dimensionless wave amplitude, $\epsilon$. For $\delta=0$, the CGS and the QGS are unstable for resonance numbers $\ell=1, 2$. For small $\epsilon$, the QGS becomes more stable with increasing $\delta$ and decreasing $h$. When $\epsilon$ increases, the influence of chaos on the stability of the QGS is analyzed for different parameters of the model, $\ell$, $\delta$ and $h$.Comment: RevTeX, 38 pages, 24 figure