An approximate moving boundary method for American option pricing

We present a method to solve the free-boundary problem that arises in the pricing of classical American options. Such free-boundary problems arise when one attempts to solve optimal-stopping problems set in continuous time. American option pricing is one of the most popular optimal-stopping problems considered in literature. The method presented in this paper primarily shows how one can leverage on a one factor approximation and the moving boundary approach to construct a solution mechanism. The result is an algorithm that has superior runtimes-accuracy balance to other computational methods that are available to solve the free-boundary problems. Exhaustive comparisons to other pricing methods are provided. We also discuss a variant of the proposed algorithm that allows for the computation of only one option price rather than the entire price function, when the requirement is such.     

Benzyltriphenylphosphonium gluta­conaldehyde

The title compound, C₂₅H₂₂P⁺·C₅H₅O₂^?, crystallizes in space group P2₁/c. The phospho­nium cations form zigzag chains with P?P distances of 6.475 (1) and 8.287 (2) Å, and are related by inversion centres. Two types of attractive edge‐to‐face phenyl interactions exist, resulting in a dominant supramolecular motif. The glutaconaldehyde anions occupy the interchain spacing and hold adjacent chains together via multiple C—­H?O hydrogen bonds. The bond‐length alternation, a parameter which reveals the non‐linear optical efficiency at the molecular level, is optimized in the chromophore anion.     

Heteropolyacid (H3PW12O40) supported MCM-41: An efficient solid acid catalyst for the green synthesis of xanthenedione derivatives

HPWA/MCM-41 mesoporous molecular sieves of appropriate ratios were prepared by loading HPWA on siliceous MCM-41 by the wet impregnation method. The prepared HPWA/MCM-41 materials were characterized by X-ray diffraction analysis (XRD) and BET surface area and FT-IR measurements. The morphology of mesoporous materials was studied by TEM observation. The catalytic activity of the above materials was tested for the condensation of dimedone (active methylene carbonyl compound) and various aromatic aldehyes under liquid phase conditions at 90 °C. The products were confirmed by FT-IR, ¹H NMR and ¹³C NMR studies. HPWA supported MCM-41 catalysts catalyses efficiently the condensation of dimedone and aromatic aldehydes in ethanol and other solvents under liquid phase conditions to afford the corresponding xanthenedione derivatives. Activities of the catalysts follow the order: HPWA/MCM-41(20 wt.%) > HPWA/MCM-41(30 wt.%) > H₃PW₁₂O₄₀·nH₂O > HPWA/MCM-41(10 wt.%) > HPWA/SiO₂ (20 wt.%) > HM (12) > Hβ (8) > Al-MCM-41 (50). Various advantages associated with these protocols include simple workup procedure, short reaction times, high product yields and easy recovery and reusability of the catalyst.     

A computational analysis of the ballistic performance of light-weight hybrid composite armors

The ability of hybrid light-weight fiber-reinforced polymer-matrix composite laminate armor to withstand the impact of a fragment simulating projectile (FSP) is investigated using a non-linear dynamics transient computational analysis. The hybrid armor is constructed using various combinations and stacking sequences of a high-strength/high-stiffness carbon fiber-reinforced epoxy (CFRE) and a high-ductility/high-toughness Kevlar fiber-reinforced epoxy (KFRE) composite laminates of different thicknesses. The results obtained indicate that at a fixed thickness of the armor both the stacking sequence and the number of CFRE/KFRE laminates substantially affect the ballistic performance of the armor. Specifically, it is found that the armor consisting of one layer of KFRE and one layer of CFRE, with KFRE laminate constituting the outer surface of the armor, possesses the maximum resistance towards the projectile-induced damage and failure. The results obtained are rationalized using an analysis of the elastic wave reflection and transmission behavior at the inter-laminate and laminate/air interfaces.     

Efficient computation of sparse structures

Basic graph structures such as maximal independent sets (MIS's) have spurred much theoretical research in randomized and distributed algorithms, and have several applications in networking and distributed computing as well. However, the extant (distributed) algorithms for these problems do not necessarily guarantee fault‐tolerance or load‐balance properties. We propose and study “low‐average degree” or “sparse” versions of such structures. Interestingly, in sharp contrast to, say, MIS's, it can be shown that checking whether a structure is sparse, will take substantial time. Nevertheless, we are able to develop good sequential/distributed (randomized) algorithms for such sparse versions. We also complement our algorithms with several lower bounds. Randomization plays a key role in our upper and lower bound results. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 322–344, 2016     

Synthesis,characterization, electrochemical and photophysical properties of bimetallic complexes of rhenium(I) and osmium(II)

Monometallic and bimetallic diimine complexes of rhenium(I) and osmium(II), [(CO)₃(bpy)Re(4,4′-bpy)](PF₆) I, [(CO)₃(bpy)Re(4,4′-bpy)Re(bpy)(CO)₃](PF₆)₂II, [Cl(bpy)₂Os(4,4′-bpy)](PF₆) III and [Cl(bpy)₂Os(4,4′-bpy)Os(bpy)₂Cl](PF₆)₂IV, and a new heterobimetallic complex of rhenium(I) and osmium(II) [(CO)₃(bpy)Re(4,4′-bpy)Os(bpy)Cl](PF₆)₂V (bpy = 2,2′-bipyridine; 4,4′-bpy = 4,4′-bipyridine) have been synthesized and characterized by various spectral techniques. The photophysical properties of all the complexes have been studied and a comparison is made between the heterobimetallic and corresponding monometallic and homobimetallic complexes. Emission and transient absorption spectral studies reveal that excited state energy transfer from the rhenium(I) chromophore (∗Re) to osmium(II) takes place. The energy transfer rate constant is found to be 8.7 × 10⁷ s⁻¹.     

Lattice effects on the spin-crossover profile of a mononuclear manganese(III) cation

Six solvated salts of a mononuclear manganese(III) complex with a chelating hexadentate Schiff base ligand are reported. One member of the series, [MnL]PF(6)?0.5?CH(3)OH (1), shows a rare low-spin (LS) electronic configuration between 10-300?K. The remaining five salts, [MnL]NO(3)?C(2)H(5)OH(2), [MnL]BF(4)?C(2)H(5)OH(3), [MnL]CF(3)SO(3)?C(2)H(5)OH (4), [MnL]ClO(4)?C(2)H(5)OH (5) and [MnL]ClO(4)?0.5?CH(3)CN (6), all show gradual incomplete spin-crossover (SCO) behaviour. The structures of all were determined at 100?K, and also at 293?K in the case of 3-6. The LS salt [MnL]PF(6)?0.5?CH(3)OH is the only member of the series that does not exhibit strong hydrogen bonding. At 100?K two of the four SCO complexes (2 and 4) assemble into 1D hydrogen-bonded chains, which weaken or rupture on warming. The remaining SCO complexes 3, 5 and 6 do not form 1D hydrogen-bonded chains, but instead exhibit discrete hydrogen bonding between cation/counterion, cation/solvent or counterion/solvent and show no significant change on warming.     

The Attenuating Effect of Beta-Carotene on Streptozotocin Induced Diabetic Vascular Dementia Symptoms in Rats

This study investigated the ameliorative effects of beta-carotene (BC) on diabetes-associated vascular dementia and its action against biomolecule oxidation. The diabetic vascular dementia (VaD) was induced by administration of nicotinamide (NA; 50 mg/kg; i.p.) and streptozotocin (STZ; 50 mg/kg; i.p.). The test compound, BC (50 and 100 mg/kg; p.o.), and the reference compound, donepezil (DP) (1 mg/kg; p.o.), were administered for 15 consecutive days. Changes in learning and memory were assessed by escape latency time (ELT) and times spent in target quadrant (TSTQ) in the Morris water maze (MWM) test. The changes in neurotransmitter, i.e., acetylcholinesterase (AChE) and oxidative stress markers, i.e., thiobarbituric acid reactive substance (TBARS) and reduced glutathione (GSH), were estimated in hippocampal tissue of the rat brain. The administration of STZ caused significant deterioration of cognitive function (decreased ELT and raised the TSTQ) as compared to the normal group. Treatment with BC and DP diminished the increased AChE activity, TBARS level and decreased GSH level caused by STZ. Thus, BC ameliorates the diabetic vascular complications in VaD due to its potential anticholinergic, antioxidative and free radical scavenging actions.