Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Random Bond Effect in the Quantum Spin System (Tl1−x_{1-x}Kx_{x})CuCl3_3

The effect of exchange bond randomness on the ground state and the field-induced magnetic ordering was investigated through magnetization measurements in the spin-1/2 mixed quantum spin system (Tl$_{1-x}$K$_{x}$)CuCl$_3$ for $x<0.36$. Both parent compounds TlCuCl$_3$ and KCuCl$_3$ are coupled spin dimer systems, which have the singlet ground state with excitation gaps ${\Delta}/k_{\rm B}=7.7$ K and 31 K, respectively. Due to bond randomness, the singlet ground state turns into the magnetic state with finite susceptibility, nevertheless, the excitation gap remains. Field-induced magnetic ordering, which can be described by the Bose condensation of excited triplets, magnons, was observed as in the parent systems. The phase transition temperature is suppressed by the bond randomness. This behavior may be attributed to the localization effect.Comment: 19 pages, 7 figures, 12 eps files, revtex, will appear in PR

Inertial waves near corotation in 3D hydrodynamical disks

This paper concerns the interaction between non-axisymmetric inertial waves and their corotation resonances in a hydrodynamical disk. Inertial waves are of interest because they can localise in resonant cavities circumscribed by Lindblad radii, and as a consequence exhibit discrete oscillation frequencies that may be observed. It is often hypothesised that these trapped eigenmodes are affiliated with the poorly understood QPO phenomenon. We demonstrate that a large class of non-axisymmetric 3D inertial waves cannot manifest as trapped normal modes. This class includes any inertial wave whose resonant cavity contains a corotation singularity. Instead, these `singular' modes constitute a continuous spectrum and, as an ensemble, are convected with the flow, giving rise to shearing waves. Lastly, we present a simple demonstration of how the corotation singularity stabilizes three-dimensional perturbations in a slender torus.Comment: 17 pages, 5 figures. MNRAS accepted. V2 - Section 5.2 moved to appendix and errors remove

Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.Comment: published version, 10 page

Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals

We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor $\omega /\Delta \omega$ ($\omega$: frequency of an x ray, $\Delta\omega$: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.Comment: 4 pages, 2 figures. Title change