Methods for the rapid solution of the pricing PIDEs in exponential and Merton models

The pricing equations for options on assets that follow jump-diffusion processes contain integrals in addition to the usual differential terms. These integrals usually make such equations expensive to solve numerically. Although Fast Fourier Transform methods can be used to to evaluate the integrals at all mesh points simultaneously, they are costly since the computational region must be extended in order to avoid problems with wrap around. Other numerical difficulties arise when the density function for the jump size is not smooth, as in the Kou double exponential model. We present new solution methods which are based on the fact that even when the problems contain time-dependent parameters the integrals often satisfy easily solved ordinary or parabolic partial differential equations. In particular, we show that by using the operator splitting method proposed by Andersen and Andreasen it is possible to reduce the solution of the pricing equation in the Kou and similar models to a sequence of ordinary differential equations at each time step. We discuss the methods and present results of numerical experiments.     

Non-separation in the mean–lower-partial-moment portfolio optimization problem

With a number of advantages, lower partial moments (LPM) serve as alternatives to variance as measures of portfolio risk. For two specific targets, a separation property holds in the context of mean–LPM portfolio optimization that allows investors to separate the decision about investment proportions among risky assets from the decision about how much to invest in risky versus risk-free assets. For other targets, however, separation is not guaranteed, and this case has not received much attention in the literature. We show in the case of non-separation that investment curves are not common to all optimizing investors, but that they are convex in (mean, LPM) space and their lower envelope is the efficient frontier. We consider the interesting behavior of investment curves and optimal risky portfolios. We also show empirically that an investor who mistakenly assumes separation holds will not experience significant excess portfolio risk in all practical cases.     

Structural, ferroelectric and optical properties of Bi2VO5.5 thin films deposited on platinized silicon {(100) Pt/TiO2/SiO2/Si} substrates

Bismuth vanadate (Bi₂VO_5.5, BVO) thin films have been deposited by a pulsed laser ablation technique on platinized silicon substrates. The surface morphology of the BVO thin films has been studied by atomic force microscopy (AFM). The optical properties of the BVO thin films were investigated using spectroscopic ellipsometric measurements in the 300–820 nm wavelength range. The refractive index (n), extinction coefficient (k) and thickness of the BVO thin films have been obtained by fitting the ellipsometric experimental data in a four-phase model (air/BVO_rough/BVO/Pt). The values of the optical constants n and k that were determined through multilayer analysis at 600 nm were 2.31 and 0.056, respectively. For fitting the ellipsometric data and to interpret the optical constants, the unknown dielectric function of the BVO films was constructed using a Lorentz model. The roughness of the films was modeled in the Brugmann effective medium approximation and the results were compared with the AFM observations. PACS 78.20.-e; 77.84.-s; 77.55.+f     

On the choice of correctors for semi-implicit Picard deferred correction methods

The goal of this study is to assess the implications of the choice of correctors for semi-implicit Picard integral deferred correction (SIPIDC) methods. The SIPIDC methods previously developed compute a high-order approximation by first computing a low-order provisional solution using a semi-implicit method and then using a first-order semi-implicit method to solve a series of correction equations, each of which raises the order of accuracy of the solution by one. In this study, we examine the efficiency of SIPIDC methods that instead use standard second-order semi-implicit methods to solve the correction equations. The accuracy, efficiency, and stability of the resulting methods are compared to previously developed methods, in the context of both nonstiff and stiff problems.     

Reductive dechlorination of atrazine using sodium-borohydride catalysed by cobalt(II) phthalocyanines

A series of functional metallophthalocyanines have been synthesized to study their role as a catalyst towards the reductive dechlorination of atrazine using sodium borohydride as a mild reducing agent. The cobalt(II) phthalocyanine bearing nitro groups at the peripheral position is the most efficient catalyst with exceptionally high catalytic activity in comparison to other functional cobalt(II) phthalocyanines.     

Quantitative analysis of cycloartane glycosides in black cohosh rhizomes and dietary supplements by RRLC-ELSD and RRLC-qTOF-MS

In this study, a fast and reproducible RRLC-ELSD method for the quantitative analysis of 17 cycloartane glycosides and the aglycone cimigenol in black cohosh rhizomes and dietary supplements has been developed. Separation of the 18 triterpenes was achieved within 16 min using reversed phase material and a gradient elution system consisting of water, acetonitrile and methanol. The method was validated for accuracy (recovery rates from 96.79% to 102.86%), precision (intra-day variation ≤5.98%, inter-day variation ≤3.74%), repeatability (R.S.D. ≤ 6.94%) and sensitivity, with detection limits below 4.0 μg/mL and quantification limits lower than 13.2 μg/mL. Calibration curves were established in the range from 5–1,000 μg/mL, with correlation coefficients higher than 0.998 for all constituents investigated. Peak purity and peak assignment were confirmed by means of RRLC-qTOF-MS and in comparison with reference compounds. Three different MS sources (ESI, APCI and APPI) were compared for their ionisation potential regarding cycloartane derivatives. One of the isolated black cohosh constituents, 24-O-acetylhydroshengmanol-3-O-α-l-arabinopyranoside, could be identified as new natural compound.     

Effect of spherical aberrations in tight focusing of higher order radially polarized beam

The effect of spherical aberration, in higher order radially polarized beam, is investigated theoretically by vector diffraction theory. It is observed that an increase in aberration results in the spreading of the intensity distribution, positional shift and the size of the generated focal pattern.