A backward dual representation for the quantile hedging of Bermudan options

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exercise date. We provide numerical illustrations

Water-Oil Partition Profiling of Ionized Drug Molecules Using Cyclic Voltammetry and a 96-Well Microfilter Plate System

Purpose. A new experimental set-up for studying partitioning of ionizable drugs at the interface between two immiscible electrolyte solutions (ITIES) by amperometry is presented. The method is quite general, as it can be applied to any charged drug molecule. Methods. The procedure is based on 96-well microfilter plates with microporous filters to support 96 organic liquid membranes. The new methodology is first validated using a series of tetra-alkylammonium ions and subsequently used to construct the ion partition diagrams of 3,5-N,N-tetramethylaniline and 2,4-dinitrophenol. The lipophilicity of these drugs was examined by potentiometry and cyclic voltammetry in the NPOE/water system. Results. Cyclic voltammetry resulted in potential-pH profiles of the studied drugs. When the aqueous phase pK a is already known, the logP NPOEof lipophilic drugs could be determined using a very little amount of solvents and drugs. The values of the partition coefficients for the neutral forms agree well with those obtained by potentiometry. Conclusions. The procedure based on commercially available 96-well microfilter plates is shown to be useful for determining logP of ionized drugs in a rapid and efficient wa

Standard partition coefficients of anionic drugs in the n-octanol/water system determined by voltammetry at three-phase electrodes

The anionic forms of 26 drugs and organic model compounds have been extensively explored in the n-octanol/ water system using voltammetry at three-phase electrodes. The objective of this study was to validate the ability of this electrochemical system to give reliable values of lipophilicity for organic ions, as well as to gain more information on the lipophilic behaviour of anions in the n-octanol/water system. Results were used to clarify the solvation mechanisms responsible for ion partitioning and to compare the information obtained in the two solvent systems n-octanol/water and 1,2-dichloroethane/water

A Comparison of the Solvation Properties of 2-Nitrophenyloctyl Ether, Nitrobenzene, andn-Octanol as Assessed by Ion Transfer Experiments

The lipophilicity of the anionic forms of drugs and model compounds was assessed by their transfer across (i) the water-2-nitrophenyloctyl ether (NPOE), (ii) the water-nitrobenzene (NB), and (iii) the water-noctanol interfaces by using the three-phase electrode technique. The lipophilicities, expressed in terms of logarithm of partition coefficients, range for the studied anions from -3.46 to 0.68 (log PA-,aq QNPOE) for NPOE, from -3.81 to 2.62 (log PA-,aq QNB ) for NB, and from -6.20 to -3.20 (log PA-,aq Qn-oct) for n-octanol. Although NPOE shares with nitrobenzene the aromatic part and with n-octanol the hydrophobic carbon chain, only very weak correlation was observed between the NPOE-based data with the n-octanol-based data, and the same is true for the correlation of the NB-based and n-octanol-based data. However, there is a strong and even linear correlation between the NPOE-based and the NB-based data

Selenium-containing heterocycles from isoselenocyanates: synthesis of 1,3-selenazoles from N-phenylimidoyl isoselenocyanates

The reaction of N-phenylbenzamides 5 with excess SOCl2 under reflux gave N-phenylbenzimidoyl chlorides 6, which, on treatment with KSeCN in acetone, yielded imidoyl isoselenocyanates of type 2. These products, obtained in almost quantitative yield, were stable in the crystalline state. They were transformed into selenourea derivatives 7 by the reaction with NH3, or primary or secondary amines. In acetone at room temperature, 7 reacted with activated bromomethylene compounds such as 2-bromoacetates, acetamides, and acetonitriles, as well as phenacyl bromides and 4-cyanobenzyl bromide to give 1,3-selenazol-2-amines of type 9 (Scheme 2). A reaction mechanism via alkylation of the Se-atom of 7, followed by ring closure and elimination of aniline, is most likely (cf. Scheme 7). In the case of selenourea derivatives 7d and 7l with an unsubstituted NH2 group, an alternative ring closure via elimination of H2O led to 1,3-selenazoles 10a and 10b, respectively (Schemes 4 and 7). On treatment with NaOH, ethyl 1,3-selenazole-5-carboxylates 9l and 9s were saponified and decarboxylated to give the corresponding 5-unsubstituted 1,3-selenazoles 12a and 12b (Scheme 6). The molecular structures of selenourea 7f and the 1,3-selenazoles 9c and 9d have been established by X-ray crystallography (Figs. 1 and 3)

Persistence of an intact endometrial matrix and vessels structure in women exposed to VA-2914, a selective progesterone receptor modulator.

Background: VA-2914 is a selective progesterone receptor modulator with potential contraceptive activity that induces amenorrhea, whereas progestins cause endometrial spotting and bleeding. This abnormal bleeding due to progestins is a consequence of focal stromal proteolysis by an increase in naked vessel size and density. Objective: Our objective was to quantify the effects of VA-2914 on endometrial vascularization, fibrillar matrix, and vascular endothelial growth factor (VEGF)-A expression in endometrial biopsies from 41 women before and after 12 wk daily treatment with a placebo, or 2.5, 5, or 10 mg VA-2914. Methods: Collagen fibrillar network was stained by silver impregnation. Vessel area, density, and structure were quantified with a computer-assisted image analysis system after double immunostaining using an anti-von Willebrand factor (endothelial cells) and an anti- smooth muscle actin (vascular smooth muscle cells) marker antibody. VEGF-A mRNAs were quantified by RT-PCR and localized by immunohistochemistry. Results: The endometrial vessels, collagen network, and mRNA levels of VEGF-A were identical during the luteal phase at baseline and in VA-2914 treated women. VEGF-A distribution was unchanged. Conclusions: VA-2914 does not alter the endometrial matrix and cells, and does not modify the endometrial vessel morphology as compared with baseline biopsies

Water-oil partition profiling of ionized drug molecules using cyclic voltammetry and a 96-well microfilter plate system

PURPOSE: A new experimental set-up for studying partitioning of ionizable drugs at the interface between two immiscible electrolyte solutions (ITIES) by amperometry is presented. The method is quite general, as it can be applied to any charged drug molecule. METHODS: The procedure is based on 96-well microfilter plates with microporous filters to support 96 organic liquid membranes. The new methodology is first validated using a series of tetra-alkylammonium ions and subsequently used to construct the ion partition diagrams of 3,5-N,N-tetramethylaniline and 2,4-dinitrophenol. The lipophilicity of these drugs was examined by potentiometry and cyclic voltammetry in the NPOE/water system. RESULTS: Cyclic voltammetry resulted in potential-pH profiles of the studied drugs. When the aqueous phase pKa is already known, the logP(NPOE) of lipophilic drugs could be determined using a very little amount of solvents and drugs. The values of the partition coefficients for the neutral forms agree well with those obtained by potentiometry. CONCLUSIONS: The procedure based on commercially available 96-well microfilter plates is shown to be useful for determining logP of ionized drugs in a rapid and efficient way

Theoretical and experimental exploration of the lipophilicity of zwitterionic drugs in the 1,2-dichloroethane/water system

PURPOSE: This work examines the lipophilic behavior of various zwitterions and shows how distribution profiles in biphasic systems and ionic partition diagrams may improve our understanding of pH-absorption profiles of drugs. METHODS: The lipophilicity of various zwitterionic drugs was examined by potentiometry and cyclic voltammetry in the 1,2-dichloroethane/water system to study the intramolecular interactions and conformational effects affecting absorption and activity of zwitterions, as well as to draw their theoretical and experimental ionic partition diagrams. RESULTS: Different theoretical partition diagrams are reported according to the tautomeric constant of the zwitterion. Shifts of apparent PKa are obtained in the ionic partition diagrams of raclopride and eticlopride and compared to the deviations from pH-absorption profile described in the literature for lipophilic drugs. The physicochemical origin of these shifts is discussed. CONCLUSIONS: The comparison between pH-absorption profiles and ionic partition diagrams of zwitterions is shown here to be of value for a better mechanistic understanding of absorption processes, thus opening new perspectives in studying pH-absorption profiles of ionizable drugs

Cyclic voltammetry of highly hydrophilic ions at a supported liquid membrane

Cyclic voltammetry has been used to study the coupling of ion transfer reactions at a liquid membrane. The liquids are either supported by a porous hydrophobic membrane (polyvinylidene difluoride, PVDF) when the organic solvent is non-volatile (o-nitrophenyloctylether) or are merely a free standing organic solvent layer such as 1,2-dichloroethane comprised between two hydrophilic dialysis membranes supporting the adjacent aqueous phases. The passage of current across the liquid membrane is associated with two ion transfer reactions across the two polarised liquid I liquid interfaces in series. It is shown that it is possible to study the transfer of highly hydrophilic ions at one interface by limiting the mass transfer of the other ion transfer reaction at the other interface. Indeed, for systems comprising an ion M in one aqueous phase and a reference ion R partitioned between the membrane and the other aqueous phase, the observed and simulated cyclic voltammograms have a half-wave potential determined by the Gibbs energy of transfer of M transferring at one interface and by the limiting mass transfer of R at the other interface. This new methodology opens a way to measure the Gibbs energy of transfer of highly hydrophilic or hydrophobic ions, which usually limits the potential window at single liquid \ liquid interfaces (ITIES). (C) 2002 Elsevier Science B.V. All rights reserve