Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting

In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Lévy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.     

A Convenient Access to Chiral Sulfonic Acids

Neomenthyl and trans myrtanyl sulfonic acids are obtained, free from inorganic salts, starting from the corresponding chiral alcohols.     

Optimized Quantitative Method for Determining Isoflavones and Equol in Bovine Digestive Fluids and Feces

Many studies have been conducted on the impact of animal feed on isoflavones and their metabolite concentrations in bovine milk, but few studies have focused on the development and validation of analytical protocols for quantifying these compounds in biological matrices other than milk and plants. The purpose of this study was to develop a method that would enable four isoflavones and equol in cows’ feces and digestive fluids to be quantified simultaneously. The method is based on aglycones released by methanolic ultrasound-assisted extraction, followed by enzymatic hydrolysis and high-performance liquid chromatography tandem–mass spectrometry analysis. The sample preparation was optimized using the Box–Behnken design. The selected extraction conditions were 80°C, 10?min, and 50% methanol for digestive fluids and 70°C, 35?min, and 60% methanol for feces. For hydrolysis, the selected conditions were 37°C, 1?h, and a pH of 6 for both matrices. The analytical method showed a good linear regression model ranging from 5 to 125?ng?mL^?1. Both inter- and intraday accuracy (≤8.5 and ≤12.3%) and precision (≤11.1 and ≤15.2%) were suitable. No matrix effects were found. There was good repeatability and extract stability for at least 4 days of storage at???20 and 6°C. All recoveries were in the acceptable range of 70–120% for both matrices, except for biochanin A in feces, where the value was approximately 43%. This sensitive and reliable method will be useful for monitoring the passage of isoflavones and equol in the digestive system of ruminants.     

Synthesis of the 1,2-Dihydro 1,2-Δ3−azaphosphorines

Abstract

1,2-Dihydro 1,2-Δ³? azaphosphorines were prepared by reaction of dichlorophenylphosphine with two equivalents of imines. 2-Oxo 1,2-azaphospholenes were also obtained in some cases.