Fourier Inversion Formulas in Option Pricing and Insurance

Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical examples are provided.      

Analyses of intrinsic inhomogeneity and metal segregation in samples of Ag–Ge–Se glasses

Ge_ySe_(1−y) glasses are semiconductors but when Ag is added above certain threshold concentration, Ag_x[Ge_ySe_(1−y)]_(100−x) glasses behave as fast ionic conductors [Ureña et al., Solid State Ionics 176 (2005) 505]. This peculiar behavior may be attributed to the intrinsically inhomogeneous nature of these glasses where zones rich in metals coexist with zones of the host material. The conductivity transformation may be ascribed to the percolation of the Ag rich phase [Pradel et al., J. Phys.: Condens. Matter 15 (2003) S1561].Ag_x[Ge_0.25Se_0.75]_(100−x) glasses either massive or as films were obtained by melt quenching and pulsed laser deposition (PLD), respectively, in compositions belonging to the Se rich corner of the ternary phase diagram. Their amorphous nature and intermediate range order was checked employing X-ray diffractometry (XRD), the short range order was characterized by extended X-ray absorption fine structure (EXAFS) (Ge and Se K absorption edge) and their microstructure was characterized by scanning electron microscopy (SEM) and small angle X-ray scattering (SAXS).     

Neural Networks in Which Synaptic Patterns Fluctuate with Time

We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1–p, respectively, in the limit p0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations.     

General transformations from multiplicative noise to additive noise

General transformations from multiplicative noise to additive noise are obtained for systems whose dynamical evolution is given by multidimensional Langevin equations.     

Boltzmann entropy for dense fluids not in local equilibrium

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f=[f(x,v)] and the total energy E. We find that S(f(t),E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(M(t))=S(M(X(t))) should hold generally for "typical" (the overwhelming majority of) initial microstates (phase points) X0 belonging to the initial macrostate M0, satisfying M(X0)=M(0). This is a consequence of Liouville's theorem when M(t) evolves according to an autonomous deterministic law.     

Structure of low-lying <Superscript>12</Superscript>C resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of ¹²C in the 3α model. We use Ali-Bodmer potentials and compare results for other potentials α-α with similar ⁸Be properties. A three-body potential is used to adjust the ¹²C resonance positions to desired values extending the applicability of the method to many-body systems decaying into three α-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two 0⁺, three 2⁺, two 4⁺, one of each of 1^±, 2^-, 3^±, 4^-, and 6⁺. The partial-wave decomposition of each resonance is calculated as a function of the hyperradius. Strong variation is found from small to large distance. The connection to previous experimental and theoretical results is discussed and agreements as well as disagreements are emphasized.     

Fast chromatographic method for the determination of dyes in beverages by using high performance liquid chromatography—Diode array detection data and second order algorithms

A fast chromatographic methodology is presented for the analysis of three synthetic dyes in non-alcoholic beverages: amaranth (E123), sunset yellow FCF (E110) and tartrazine (E102). Seven soft drinks (purchased from a local supermarket) were homogenized, filtered and injected into the chromatographic system. Second order data were obtained by a rapid LC separation and DAD detection. A comparative study of the performance of two second order algorithms (MCR-ALS and U-PLS/RBL) applied to model the data, is presented. Interestingly, the data present time shift between different chromatograms and cannot be conveniently corrected to determine the above-mentioned dyes in beverage samples. This fact originates the lack of trilinearity that cannot be conveniently pre-processed and can hardly be modelled by using U-PLS/RBL algorithm. On the contrary, MCR-ALS has shown to be an excellent tool for modelling this kind of data allowing to reach acceptable figures of merit. Recovery values ranged between 97% and 105% when analyzing artificial and real samples were indicative of the good performance of the method. In contrast with the complete separation, which consumes 10 mL of methanol and 3 mL of 0.08 mol L⁻¹ ammonium acetate, the proposed fast chromatography method requires only 0.46 mL of methanol and 1.54 mL of 0.08 mol L⁻¹ ammonium acetate. Consequently, analysis time could be reduced up to 14.2% of the necessary time to perform the complete separation allowing saving both solvents and time, which are related to a reduction of both the costs per analysis and environmental impact.     

Photopolymerization initiated by carbonyl compounds. VII. Solvent effects on biacetyl photoinitiation

Biacetyl is solvated by methanol or water giving an α-substituted alkanone. Irradiation of the solvated species at 300 nm in the presence of vinyl acetate or vinyl pyrrolidone, produces a significant amount of polymer. The photoprocesses leading to active free radicals are considered to be a type I photocleavage of the α-substituted alkanone.     

Simultaneous determination of pesticides, biopesticides and mycotoxins in organic products applying a quick, easy, cheap, effective, rugged and safe extraction procedure and ultra-high performance liquid chromatography-tandem mass spectrometry

A method for the simultaneous determination of pesticides, biopesticides and mycotoxins from organic products was developed. Extraction of more than 90 compounds was evaluated and performed by using a modified QuEChERS-based (acronym of Quick, Easy, Cheap, Effective, Rugged, and Safe) sample preparation procedure. The method was based on a single extraction with acidified acetonitrile, followed by partitioning with salts, avoiding any clean-up step prior the determination by ultra-high performance liquid chromatography/tandem quadrupole mass spectrometry (UHPLC–MS/MS). Validation studies were carried out in wheat, cucumber and red wine as representative matrixes. Recoveries of the spiked samples were in the range between 70 and 120% (with intra-day precision, expressed as relative standard deviation, lower than 20%) for most of the analysed compounds, except picloram and quinmerac. Inter-day precision, expressed as relative standard deviation, was lower than 24%. Limits of quantification were lower than 10 μg kg⁻¹ and the developed method was successfully applied to the analysis of organic food products, detecting analytes belonging to the three types of compounds.