Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).     

Two stage magnetic ordering and spin idle behavior of the coordination polymer Co3(OH)2(C4O4)2·3H2O determined using neutron diffraction

We report the magnetic structure of two of the magnetically ordered phases of Co(3)(OH)(2)(C(4)O(4))(2)·3H(2)O, a coordination polymer that consists of a triangular framework decorated with anisotropic Co(II) ions. The combination of neutron diffraction experiments and magnetic susceptibility data allows us to identify one phase as displaying spin idle behavior, where only a fraction of the moments order at intermediate temperatures, while at the lowest temperatures the system orders fully. This novel magnetic behavior is discussed within the framework of a simple Hamiltonian and representational analysis and rationalizes this multiphase behavior by considering the combination of frustration and anisotropy.     

Structure and dynamics of the fast lithium ion conductor "Li7La3Zr2O12"

The solid lithium-ion electrolyte "Li(7)La(3)Zr(2)O(12)" (LLZO) with a garnet-type structure has been prepared in the cubic and tetragonal modification following conventional ceramic syntheses routes. Without aluminium doping tetragonal LLZO was obtained, which shows a two orders of magnitude lower room temperature conductivity than the cubic modification. Small concentrations of Al in the order of 1 wt% were sufficient to stabilize the cubic phase, which is known as a fast lithium-ion conductor. The structure and ion dynamics of Al-doped cubic LLZO were studied by impedance spectroscopy, dc conductivity measurements, (6)Li and (7)Li NMR, XRD, neutron powder diffraction, and TEM precession electron diffraction. From the results we conclude that aluminium is incorporated in the garnet lattice on the tetrahedral 24d Li site, thus stabilizing the cubic LLZO modification. Simulations based on diffraction data show that even at the low temperature of 4 K the Li ions are blurred over various crystallographic sites. This strong Li ion disorder in cubic Al-stabilized LLZO contributes to the high conductivity observed. The Li jump rates and the activation energy probed by NMR are in very good agreement with the transport parameters obtained from electrical conductivity measurements. The activation energy E(a) characterizing long-range ion transport in the Al-stabilized cubic LLZO amounts to 0.34 eV. Total electric conductivities determined by ac impedance and a four point dc technique also agree very well and range from 1 × 10(-4) Scm(-1) to 4 × 10(-4) Scm(-1) depending on the Al content of the samples. The room temperature conductivity of Al-free tetragonal LLZO is about two orders of magnitude lower (2 × 10(-6) Scm(-1), E(a) = 0.49 eV activation energy). The electronic partial conductivity of cubic LLZO was measured using the Hebb-Wagner polarization technique. The electronic transference number t(e-) is of the order of 10(-7). Thus, cubic LLZO is an almost exclusive lithium ion conductor at ambient temperature.     

Living radical polymerization of vinyl chloride initiated with iodoform and catalyzed by nascent Cu0/tris(2‐aminoethyl)amine or polyethyleneimine in water at 25 °C proceeds by a new competing pathways mechanism

The first example of living radical polymerization of vinyl chloride carried out in water at 25 °C is reported. This polymerization was initiated by iodoform and catalyzed by nascent Cu⁰ produced by the disproportionation of Cu^I in the presence of strongly Cu^II binding ligands such as tris(2‐aminoethyl)amine or polyethyleneimine. The resulting poly(vinyl chloride) was free of structural defects, had controlled molecular weight and narrow molecular weight distribution, contained two ～CHClI active chain ends, and had a higher syndiotacticity (62%) than the one obtained by conventional free‐radical polymerization at the same temperature (56%). This novel polymerization proceeds, most probably, by a combination of competitive pathways that involves activation by single electron transfer mediated by nascent Cu⁰ and degenerative chain transfer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3283–3299, 2003     

A Convex Envelope Formula for Multilinear Functions

Convex envelopes of multilinear functions on a unit hypercube arepolyhedral. This well-known fact makes the convex envelopeapproximation very useful in the linearization of non-linear 0–1programming problems and in global bilinear optimization. This paperpresents necessary and sufficient conditions for a convex envelope to be apolyhedral function and illustrates how these conditions may be used inconstructing of convex envelopes. The main result of the paper is a simpleanalytical formula, which defines some faces of the convex envelope of amultilinear function. This formula proves to be a generalization of the wellknown convex envelope formula for multilinear monomial functions.     

Research on orotron oscillator with dispersive open resonant system

Theoretical and experimental results of an investigation into a new resonant system have been obtained. This system is named the sphere-corner-echelette open resonator (SCEOR) due to the employment of a mirror that was formed by two echelettes at the angles of 45° to the resonator axis. It turns ont that this resonator is excited on the specific modes not unique to others oscillating systems. There are presented the results of the experimental research of the orotron oscillator with the SCEOR. The spectrum of this device contains only the fundamental modes such as theT E M ₀₀₆,T E M ₀₀₇,T E M ₀₀₈. The efficiency of the orotron is improved, when all other factors are the same the orotron with a much used sphere-cylindrical open resonator.     

An Optimal Series Expansion of the Multiparameter Fractional Brownian Motion

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal. This work is supported in part by the Foundation for Knowledge and Competence Development and Sparbanksstiftelsen Nya.     

Carbon-nanotube-based saturable absorbers for near infrared solid state lasers

We demonstrate the passive mode-locking of a diode-pumped Nd⁺³:YAG (central wavelength: 1.32 μm; pulse duration: 50 ps; output energy: up to 70 μJ) laser using a polymer film containing single-wall carbon nanotubes. The mode-locking regime is stable at a pump repetition rate of up to 1 kHz. We also investigate the temporal evolution of the light-induced absorption change of the polymer film containing carbon nanotubes in the spectral range of 1.3–1.5 μm by femtosecond time-resolved pump-probe measurements. The measurements reveal that light-induced transmission exhibits fast and slow components that last 280 fs and more than 10 ps, respectively. The third-order susceptibility of the polymer film containing single wall carbon nanotubes is as high as 10⁻¹¹ esu.     

Orientational coupling amplification in ferroelectric nematic colloids

We investigated the physical properties of low concentration ferroelectric nematic colloids, using calorimetry, optical methods, infrared spectroscopy, and capacitance studies. The resulting homogeneous colloids possess a significantly amplified nematic orientational coupling. We find that the nematic orientation coupling increases by approximately 10% for particle concentrations of 0.2%. A manifestation of the increased orientational order is that the clearing temperature of a nematic colloid increases by up to 40 degrees C compared to the pure liquid crystal host. A theoretical model is proposed in which the ferroelectric particles induce local dipoles whose effective interaction is proportional to the square of the orientational order parameter.     

The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.