Multi-Scale Time-Changed Birth Processes for Pricing Multi-Name Credit Derivatives

Abstract

We develop two parsimonious models for pricing multi-name credit derivatives. We derive closed form expression for the loss distribution, which then can be used in determining the prices of tranche and index swaps and more exotic derivatives on these contracts. Our starting point is the model of Ding et al., 2008, which takes the loss process as a time-changed birth process. We introduce stochastic parameter variations into the intensity of the loss process and use the multi-time scale approach of Fouque et al., 2003 Fouque, J.-P., Papanicolaou, G., Sircar, R. and Solna, K. 2003. Multiscale stochastic volatility asymptotics. SIAM Journal of Multiscale Modeling and Simulation, 2(1): 22–42.  [Google Scholar] and obtain explicit perturbation approximations to the loss distribution. We demonstrate the competence of our approach by calibrating it to the CDX index data.     

The Use of Microporous Divinyl Benzene Copolymer for Yeast Cell Immobilization and Ethanol Production in Packed-Bed Reactor

Microporous divinyl benzene copolymer (MDBP) was used for the first time as immobilization material for Saccharomyces cerevisiae ATCC 26602 cells in a bed reactor and ethanol production from glucose was studied as a model system. A very homogenous thick layer of yeast cells were seen from the scanning electron micrographs on the outer walls of biopolymer. The dried weight of the cells was found to be approximately 2 g per gram of cell supporting material. Hydrophobic nature of polymer is an important factor increasing cell adhesion on polymer pieces. The dynamic flow conditions through the biomaterial due to its microporous architecture prevented exopolysaccharide matrix formation around cells and continuous washing out of toxic metabolites and dead and degraded cells from the reactor provided less diffusional limitations and dynamic living environment to the cells. In order to see the ethanol production performance of immobilized yeast cells, a large initial concentration range of glucose between 6.7 and 300 g/l was studied at 1 ml/min in continuous packed-bed reactor. The inhibition effect of glucose with increasing initial concentration was observed at above 150 g/l, a relatively high substrate concentration. The continuous fluid flow around the microenvironment of the attached cells and mass transferring ability of cell immobilized on MDBP can help in decreasing the inhibition effect of ethanol accumulation and high substrate concentration in the vicinity of the cells.     

(E)‐2‐[(4‐Chlorophenyl)iminomethyl]‐5‐methoxyphenol and (E)‐2‐[(2‐chlorophenyl)iminomethyl]‐5‐methoxyphenol: X‐ray and DFT‐calculated structures

The crystal structures of the title 4‐chlorophenyl, (I), and 2‐chlorophenyl, (II), compounds, both C₁₄H₁₂ClNO₂, have been determined using X‐ray diffraction techniques and the molecular structures have also been optimized at the B3LYP/6‐31 G(d,p) level using density functional theory (DFT). The X‐ray study shows that the title compounds both have strong intramolecular O—H...N hydrogen bonds and that the crystal networks are primarily determined by weak C—H...π and van der Waals interactions. The strong intramolecular O—H...N hydrogen bond is evidence of the preference for the phenol–imine tautomeric form in the solid state. The IR spectra of the compounds were recorded experimentally and also calculated for comparison. The results from both the experiment and theoretical calculations are compared in this study.     

Chemical Effect on K Shell X-ray Fluorescence Parameters and Radiative Auger Ratios of Co, Ni, Cu, and Zn Complexes

对钴、镍、铜、锌元素组成的不同配合物K壳层X射线的产生截面、谱线强度比、俄歇辐射强度比进行了测定,同时研究了化学效应对K壳荧光参数和俄歇辐射强度比的影响,并根据电荷转移过程解释了这些参数的变化. 采用59.5 keV的γ射线²⁴¹Am的环形放射源对样品进行激发. 用分辨率为150eV的Ultra-LEGe探测器在5.9 keV测定样品产生的K壳X射线.     

Sandwiched trilayer of Bethe lattices in the form of spin-(1/2,1,1/2)

The sandwiched trilayer of Bethe lattices in the form of the spins with spin-(1/2,1,1/2) Ising model is studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic type bilinear interactions between the nearest-neighbor (NN) spins. The ground-state (GS) phase diagrams are obtained and it was found that the model presents six different GS phase configurations. In order to obtain the phase diagrams, the thermal variations of the order-parameter, spin-spin correlation functions and free energy are analyzed and different topological phase diagrams are obtained. It was found that the system exhibits different critical behaviors such as, second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3,4 and 6.     

3‐Hydro­xy‐6‐[(4‐hydroxy­phenyl­amino)­methyl­ene]­cyclo­hexa‐2,4‐dienone and 2‐hydroxy‐6‐[(4‐hydroxy­phenyl­amino)­methyl­ene]­cyclo­hexa‐2,4‐dienone

The title compounds, both C₁₃H₁₁NO₃, exist as the keto–amine tautomers, and the formal hydroxyl H atoms, which display strong intramolecular hydrogen bonds, are located on the N atoms. This is a verification of the preference for the keto–amine tautomeric form in the solid state. The 2‐hydroxy isomer has two independent mol­ecules, with the mol­ecules linked by intramolecular N—H⋯O and O—H⋯O and intermolecular O—H⋯O hydrogen bonds into three‐dimensional networks.     

Desynchronization of Pedal Motion: Crystallographic and Theoretical Study of (<Emphasis Type="Italic">E</Emphasis>)-4-[(4-ethylphenyl)diazenyl]-2-methylphenol

Abstract  The single crystal X-ray diffraction analysis of the title compound, C₁₅H₁₆N₂O, reveals that its molecules exhibit whole-molecule disorder at both crystal lattice sites due to pedal motion in solid state. The compound crystallizes in the monoclinic space group P 2₁/c with a = 20.5504(14) ?, b = 10.8887(5) ?, c = 12.0191(8) ? and β = 96.927(5)°. While major pedal conformers of the compound in solid state are stabilized by intermolecular O–H···N type hydrogen bonds leading to the formation of C(7) chains at Site 1 and C(8) chains at Site 2 along [0 1 0] axis, C–H···π type intermolecular interactions between major and minor conformers also serve to stabilize minor pedal conformers. An interesting feature about the crystal structure is that pedal conformers at Site 1 have two different occupancy factors arising from desynchronization of pedal motion along [2 1 0] direction in crystal phase. Quantum chemical calculations at the B3LYP/6-31++G** level suggest that the desynchronization of pedal motions make more unstable pedal conformers at Site 1 than those at Site 2. Index Abstract  Molecular and crystal structure of (E)-4-[(4-ethylphenyl)diazenyl]-2-methylphenol, C₁₆H₁₈N₂O, indicate desynchronization of pedal motion and the quantum chemical calculations at level of B3LYP/6-31++G** suggest that desynchronization of pedal motions make more unstable pedal conformers.      

A unified treatment of dividend payment problems under fixed cost and implementation delays

In this paper we study the dividend optimization problem for a corporation or a financial institution when the management faces (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein–Uhlenbeck and square-root processes. Since the cash flow structure of different companies have different qualitative behaviors, it makes sense to use different diffusions to model them. The delay causes significant difficulties to the optimization problem since the cash reservoir fluctuates during the delay period. We provide a uniform mathematical framework to analyze all the models and provide optimal threshold strategies at which the management initiates actions, i.e., declaration and payment of dividends. Our solution depends on a new characterization of the value function for one-dimensional diffusions and provide easily implementable algorithms to find the optimal control and the value function.