Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

The option pricing problem when the asset is driven by a stochastic volatility process and in the presence of transaction costs leads to solving a nonlinear partial differential equation. The nonlinear term in the PDE reflects the presence of transaction costs. Under a particular market completion assumption we derive the nonlinear PDE whose solution may be used to find the price of options. In this paper under suitable conditions, we give an algorithmic scheme to obtain the solution of the problem by an iterative method and provide numerical solutions using the finite difference method.     

Atiyah sequences,connections and characteristic forms for principal bundles over groupoids and stacks

We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah exact sequences associated with transversal tangential distributions.     

On abelian principal bundles

Let T be a complex torus and E _T a holomorphic principal T-bundle over a connected complex manifold M. We prove that the total space of E _T admits a K?hler structure if and only if M admits a K?hler structure and E _T admits a flat holomorphic connection whose monodromy preserves a K?hler form on T. If E _T admits a K?hler structure, then is isomorphic to . Received: 2 September 2005     

Rhenium chemistry of azooximes: oxygen atom transfer, azoimine chelation, and imine-oxime contrast

The concerned azooximes (L1OH, 1) are of type p-X-C6H4C(N2Ph)(NOH) (X = H, Me, Cl). The reaction of [Re(MeCN)Cl3(PPh3)2] with [Ag(L1OH)(L1O)] in cold dichloromethane-acetonitrile solvent has furnished the green colored ionized azoimine complex [ReV(O)Cl(PPh3)2(L1)](PF6), 2. In effect L1O- has undergone oxidative addition, the oxygen atom being transferred to the metal site. Upon treatment of [ReV(NPh)Cl3(PPh3)2] with L1OH in solution, the neutral azoimine complex [ReV(NPh)Cl3(L1H)], 3, resulted due to the spontaneous transfer of the oxime oxygen atom to a PPh3 ligand, which is eliminated as OPPh3. In contrast, the oxime of 2-acetylpyridine (L2OH, 4) did not undergo oxygen atom transfer and simply afforded the imine-oxime complex [ReV(NC6H4Y)Cl2(PPh3)(L2O)], 5, upon reacting with [ReV(NC6H4Y)Cl3(PPh3)2] (Y = H, Me, Cl). The spectral and electrochemical properties of 2, 3, and 5 and the structures of three representative compounds are reported. In the cation of 2 (X = H) the two PPh3 ligands lie trans to each other and the equatorial plane is defined by the five-membered azoimine chelate ring and the oxo and chloro ligands. The oxo ligand which forms a model triple bond (Re-O length 1.616(6) A) lies cis to the imine-N atom. In 3 (X = Cl) the ReCl3 fragment has meridional geometry and the imido nitrogen lies trans to the imine nitrogen of the planar azoimine chelate ring. In 5 x H2O (Y = Me), the Cl, oximato-N, and P atoms define an equatorial plane and the pyridine-N lies trans to the imido-N. The water of crystallization is hydrogen bonded to the oximato oxygen atom (O...O, 2.829(5) A). Reaction models in which chelation of the azooxime precedes oxygen atom transfer are proposed on the basis of oxophilicity of trivalent rhenium, Lewis acid activity of pentavalent rhenium, electron withdrawal by the azo group, and observed relative disposition of ligands in products.     

Oximato bridged RhIII2MII and RhIIIMI species (MII = Mn, Co, Ni; MI = Cu, Ag)

The reaction of [RhCl₂(HPhL)(PhL)] with M^II(ClO₄)₂·6H₂O in presence of alkali has furnished trinuclear [RhCl₂(PhL)₂]₂M(H₂O)₂·H₂O (HPhL is phenylazobenzaldoxime; M = Mn, Co, Ni). A similar reaction with M^I(PPh₃)₂NO₃ yielded binuclear [RhCl₂(PhL)₂]M(PPh₃)₂ (M = Cu, Ag). In these molecules the oximato group acts as a bridge between Rh^III (bonded at N) and M^II or M^I (bonded at O). In structurally characterized [Rh^IIICl₂(PhL)₂]₂Mn(H₂O)₂.H₂O the centrosymmetric distorted octahedral MnO₆ coordination sphere is spanned by four oximato oxygen atoms and two water molecules lying in trans position. In the lattice the neighbouring molecules are held together by H₂O⋯H₂O⋯H₂O hydrogen bonds generating infinite zigzag chains. The manganese atoms lie parallel to the C-axis, the shortest Mn...Mn distance being 7.992 ?. Magnetic exchange interactions if any are small as seen in room temperature magnetic moments. The manganese system displays a strong EPR signal near g = 2.00. In the complex [RhCl₂(PhL)₂]Cu(PPh₃)₂ the copper atom is coordinated to two oximato oxygen atoms and the two phosphorus atoms in a distorted tetrahedral geometry. The softness of the phosphine ligand is believed to sustain the stable coordination of hard oximato oxygen to soft Cu^I. The coordination sphere of the RhIII atom in both the complexes is uniformly trans-RhN₄Cl₂.     

Microchip electrophoresis of N-glycans on serpentine separation channels with asymmetrically tapered turns

We designed and fabricated microfluidic devices with serpentine separation channels and asymmetrically tapered turns, thus allowing high efficiency separations and minimizing band broadening associated with the “racetrack” effect. We evaluated the performance of these devices by measuring the variation in separation efficiency with separation length, electric field strength, taper ratio of the turns, and number of turns. N‐Glycans derived from ribonuclease B and labeled with 8‐aminopyrene‐1,3,6‐trisulfonic acid were electrophoretically separated on serpentine channels with separation lengths of 11, 18, 22, and 36 cm at electric field strengths from 750 to 1750 V/cm. Separations on the 36‐cm channel produced plate numbers up to 940 000 with an analysis time under 3.1 min, whereas separations on the 22‐cm channel had a shorter analysis time (less than 1.25 min), still with respectable efficiencies (up to 600 000 plates). Turn‐induced dispersion was minimized with taper ratios 2 and 3, whereas having two or four 180° turns along with the separation length did not impact the overall efficiency. The developed device was used to analyze native and desialylated N‐glycans derived from the blood serum of an ovarian cancer patient and a disease‐free individual. Separation efficiencies similar to that achieved with the model glycans from ribonuclease B were attained for these biological samples.     

One-pot multicomponent synthesis of diversely substituted 2-aminopyrroles. A short general synthesis of rigidins A, B, C, and D

Privileged medicinal scaffolds based on the structures of tetra- and pentasubstituted 2-aminopyrroles were prepared via one-pot multicomponent reactions of structurally diverse aldehydes and N-(aryl-, hetaryl-, alkylsulfonamido)acetophenones with activated methylene compounds. This methodology was used in a four-step synthesis of alkaloids rigidins A, B, C, and D in overall yields of 61%, 58%, 60%, and 53%, respectively. Of these, rigidins B, C, and D were synthesized for the first time.