The quintessential option pricing formula under Lévy processes

The basic digital method for option pricing developed in Ingersoll [J. Ingersoll, Digital contracts: Simple tools for pricing complex derivatives, Journal of Business 73 (1) (2000) 67–88] and Buchen and Skipper [P. Buchen, M. Skipper, The quintessential option pricing formula, School of Mathematics and Statistics, University of Sydney, 2003, pp. 1–31] is generalized to a Lévy environment. The approach is combined with the mathematical methodology of Boyarchenko and Levendorski [S.I. Boyarchenko, S.Z. Levendorski, Non-Gaussian Merton–Black–Scholes theory, World Scientific, 2002] that employs pseudo-differential operators whose symbol is expressed in terms of the characteristic exponent of the underlying Lévy process. Some new valuation formulas are obtained.     

Mathematics Teaching in Italy: A Cross-Cultural Video Analysis

This study investigates the cultural nature of teaching. It compares a sample of 39 videotaped Italian mathematics lessons to German, Japanese, and U.S. lessons videotaped in TIMSS. This study expands on earlier work that was based on a smaller sample; analysis is also extended to the nature of the mathematical content presented. The results confirm the existence of an Italian cultural pattern for mathematics teaching, whose features we outline here. Italian teachers prefer whole-class instruction to individual seatwork; they engage in teacher talk/demonstration to transmit information; and they often call on students to solve problems at the board before the rest of the class. Italian lessons are characterized by the inclusion of a large number of mathematical principles and properties. These are explained 50% of the time, and simply stated the rest of the time. This study adds yet another perspective from which mathematics teaching can be studied, and, by acknowledging the difficulty to change cultural practices, it offers practical implications for teacher learning.     

A comprehensive mathematical approach to exotic option pricing

This work illustrates how several new pricing expressions for exotic options can be derived within a Lévy framework by employing a unique pricing expression. To the purpose, a unifying formula is obtained by solving some nested Cauchy problem for pseudodifferential equations generalizing Black–Scholes PDE. The main result extends (Agliardi R. The quintessential option pricing formula under Lévy processes. Applied Mathematics Letters 2009; 22:1626‐1631) and is a powerful tool for generating new valuation expressions. Several examples of pricing formulas under the Lévy processes are provided to illustrate the flexibility of the method. Some of them are new in the financial literature. Finally, many existing pricing formulas of the traditional Gaussian model are easily obtained as a by‐product. Copyright © 2012 John Wiley & Sons, Ltd.     

Trajectories Joining Two Submanifolds under the Action of Gravitational and Electromagnetic Fields on Static Spacetimes

In this paper we present existence and multiplicity results for orthogonal trajectories joining two submanifolds under the action of gravitational and electromagnetic fields on static spacetimes. These trajectories are critical points of unbounded functionals and they can be found by using a variant of the saddle point theorem and the relative category theory.     

Group-selective determination of total N-nitroso compounds in nitrate-containing human urine samples

A group-selective method for the determination of total N-nitroso compounds (NOC) has been adapted for analysing human urine samples. Nitrate was first removed from urine by an anion-exchange procedure that prevented the significant loss of various added reference NOC and unidentified urinary NOC. The total NOC were then determined by injecting the urine sample (nitrate content less than 1 mmol l-1) or anion-exchange eluate into refluxing ethyl acetate containing either acetic acid for determining heat and acetic acid labile thermal energy analyser responsive compounds (TAC) or into hydrogen bromide for the determination of TAC and NOC. The nitrogen monoxide levels released were measured using thermal energy analysis with chemiluminescence detection, and the differnce between the two determinations represented the concentrations of NOC. The optimum conditions for preventing artefactual nitrosation in urine samples by the addition of sodium hydroxide or sulphamic acid without decomposition of NOC were determined. The influence of time and storage conditions on NOC stability was investigated. Fifteen urine samples collected from volunteers dosed with proline were analysed for total NOC and N-nitrosamino acids revealing a preponderance of unknown NOC. The determination of total NOC in human urine using this group-selective method offers a new approach to the estimation of human exposure to NOC and to isolate hitherto unknown NOC and their metabolites.     

Asymmetric synthesis of an N-acylpyrrolidine for inhibition of HCV polymerase

A practical asymmetric synthesis of a highly substituted N-acylpyrrolidine on multi-kilogram scale is described. The key step in the construction of the three stereocenters is a [3+2] cycloaddition of methyl acrylate and an imino ester prepared from l-leucine t-butyl ester hydrochloride and 2-thiazolecarboxaldehyde. The cycloaddition features novel asymmetric catalysis via a complex of silver acetate and a cinchona alkaloid, particularly hydroquinine, with complete diastereomeric control and up to 87% enantiomeric control. The alkaloid serves as a ligand as well as a base for the formation of the azomethine ylide or 1,3-dipole. Experiments have shown that the hydroxyl group of hydroquinine is a critical element for the enantioselectivities observed. The cycloaddition methodology is also applicable to methylvinyl ketone, providing access to either alpha- or beta-epimers of 4-acetylpyrrolidine depending on the reaction conditions utilized. The synthesis also highlights an efficient N-acylation, selective O- versus N-methylation, and a unique ester reduction with NaBH4-MeOH catalyzed by NaB(OAc)3H that not only achieves excellent chemoselectivity but also avoids formation of the undesired but thermodynamically favored epimer. The highly functionalized target is synthesized in seven linear steps from l-leucine t-butyl ester hydrochloride with all three isolated intermediates being highly crystalline.     

Regioselective Glycosylation Strategies for the Synthesis of Group Ia and Ib Streptococcus Related Glycans Enable Elucidating Unique Conformations of the Capsular Polysaccharides

Group B Streptococcus serotypes Ia and Ib capsular polysaccharides are key targets for vaccine development. In spite of their immunospecifity these polysaccharides share high structural similarity. Both are composed of the same monosaccharide residues and differ only in the connection of the Neu5Acα2-3Gal side chain to the GlcNAc unit, which is a β1-4 linkage in serotype Ia and a β1-3 linkage in serotype Ib. The development of efficient regioselective routes for GlcNAcβ1-3[Glcβ1-4]Gal synthons is described, which give access to different group B Streptococcus (GBS) Ia and Ib repeating unit frameshifts. These glycans were used to probe the conformation and molecular dynamics of the two polysaccharides, highlighting the different presentation of the protruding Neu5Acα2-3Gal moieties on the polysaccharide backbones and a higher flexibility of Ib polymer relative to Ia, which can impact epitope exposure.     

Expedient synthesis of pseudo-Pro-containing peptides: towards constrained peptidomimetics and foldamers

The reaction of sulfonyl peptides containing L- or D-configured Ser or Thr with bis(succinimidyl) carbonate in the presence of a catalytic amount of a base affords, in solution or in the solid phase, the corresponding peptides with one or two, consecutive or alternate oxazolidin-2-ones (Oxd). The Oxd ring can be regarded to as a pseudo-Pro with an exclusively trans conformation of the preceding peptide bond; homochiral Oxd-containing peptides adopt extended conformations, while the presence of a D-configured Oxd favours folded conformations.     

Baeyer-Villiger oxidation in supercritical CO2 with potassium peroxomonosulfate supported on acidic silica gel

Supercritical carbon dioxide (scCO2) is an efficient reaction medium to perform the Baeyer-Villiger oxidation with hydrated silica-supported potassium peroxomonosulfate (h-SiO2.KHSO5) under flow-through conditions. Hydration modulates the reactivity of the active surface by softening the acidity of the KHSO4 present in the supported reagent. The reaction in scCO2 is much more efficient than in n-hexane under similar conditions, which is attributed to better transport and solvating properties of the supercritical medium with regard to n-hexane.