Credit Risk Monte Carlos Simulation Using Simplified Creditmetrics' Model: the joint use of importance sampling and descriptive sampling

Monte Carlo simulation is implemented in some of the main models for estimating portfolio credit risk, such as CreditMetrics, developed by Gupton, Finger and Bhatia (1997). As in any Monte Carlo application, credit risk simulation according to this model produces imprecise estimates. In order to improve precision, simulation sampling techniques other than traditional Simple Random Sampling become indispensable. Importance Sampling (IS) has already been successfully implemented by Glasserman and Li (2005) on a simplified version of CreditMetrics, in which only default risk is considered. This paper tries to improve even more the precision gains obtained by IS over the same simplified CreditMetrics' model. For this purpose, IS is here combined with Descriptive Sampling (DS), another simulation technique which has proved to be a powerful variance reduction procedure. IS combined with DS was successful in obtaining more precise results for credit risk estimates than its standard form.

Photoreactive titanate nanomaterials for water purification systems

University of Technology, Sydney. Faculty of Engineering and Information Technology.Increasing water scarcity and environmental considerations are calling for more effective means to purify industrial and urban wastewaters. Advanced oxidation processes are able to effectively remove many persistent and toxic pollutants from water to enable the use and reuse of impaired quality raw water sources. Among these processes, heterogeneous photocatalysis has some notable inherent advantages, such as relative process simplicity, and the minimal generation of waste streams. Unfortunately, the commercially available photocatalysts show poor efficiency in the utilisation of natural solar radiation and are difficult to separate and recover from treated water, which results in high operational costs. In order to alleviate these recognised problems, this thesis explored an improved method of material synthesis to produce nanomaterials with desirable properties. The investigation of peroxide method at high pH values showed that this facile approach offers great potential for the fabrication of various nanoparticles, nanostructures, and thin films deposits. The shape, size, structure and surface properties of the resulting photocatalysts were simply controlled through the process pH, the time of reaction, and the chemical composition of the solvent base. Both partial and complete dissolution of the precursors was accomplished to fabricate various, crystalline and amorphous anatase and alkali titanate end products. The use of ammonium hydroxide base was more advantageous, since it provided a very simple means to achieve simultaneous N doping. Effective N-doping of Degussa P25 commercial photocatalyst was simply achieved using highly concentrated (25%) ammonium hydroxide base in 24 h time at room temperature in an open reactor. The raw product slurries were neutralised with acid, washed with water, and aged until dry at 75 °C. Additional doping (co-doping) with Ag was achieved by adding AgNO3 to the raw slurries. The resulting nanoparticles had elongated rod and needle-like shapes, 2-3 times larger specific surface area (92.9-144.6 m2g-1) than the precursor P25, and 5.4-6.5 nm mesopore sizes. These photocatalysts were remarkably effective in the photobleaching of Methylene Blue under visible light, and simulated solar light illuminations. Therefore, this method is suitable to improve the performance of currently available commercial photocatalysts. Na-titanate microspheres with 700-800 nm diameter were produced at low (25-80 ◦C) temperatures using NaOH for base, and P25 precursor in the peroxide method. Both the raw and calcined products showed very high adsorption affinity towards Methylene Blue dye, and were also capable of its degradation under UV light without minimal loss of performance after five complete treatment cycles. The calcined product showed higher catalytic activity, and could be fully recovered from the spent slurry by gravity settling. Exchanging Na with H in titanates microspheres in HCl solution resulted in the formation of hydrogen-titanate nanofibres, which were transformed into anatase nanofibres after annealing at 550 °C for 6 h. The nanofibres had average specific surface area of 31.5 m2/g, average pore volume of 0.10 cm3/g and average pore size of 50 Å. These products also were effective adsorbent of the model pollutant and adsorbents and good photocatalyst under simulated solar light illumination. No reduction in photocatalytic activity was observed over three complete treatment cycles, and the effective separation of nanofibres was achieved by gravity settling resulting in low residual solution turbidity. Such nanofibres may also be used to produce paper-like photoreactive filter materials. An easily separable fibrous photocatalyst was produced by depositing H-titanate nanofibres on wool fibres serving as bio-template. The calcined end-product showed anatase crystal phase and nanofibrous morphology (about 50 μm length and 9.5 μm diameter), having about 24 m2/g specific surface area with mesoporous characteristics. These nanofibres were effective in the photocatalytic degradation of humic acid model pollutant solution under UV light irradiation. The performance of this photocatalyst showed only a small decrease after three complete treatment cycles, and the microfibres were easily separated from the treated solution by sedimentation with very low supernatant turbidity

Out-Of-The_Money Monte Carlo Simulation Option Pricing: the join use of Importance Sampling and Descriptive Sampling

As in any Monte Carlo application, simulation option valuation produces imprecise estimates. In such an application, Descriptive Sampling (DS) has proven to be a powerful Variance Reduction Technique. However, this performance deteriorates as the probability of exercising an option decreases. In the case of out of the money options, the solution is to use Importance Sampling (IS). Following this track, the joint use of IS and DS is deserving of attention. Here, we evaluate and compare the benefits of using standard IS method with the joint use of IS and DS. We also investigate the influence of the problem dimensionality in the variance reduction achieved. Although the combination IS+DS showed gains over the standard IS implementation, the benefits in the case of out-of-the-money options were mainly due to the IS effect. On the other hand, the problem dimensionality did not affect the gains. Possible reasons for such results are discussed.

Characterisation of titanium tetrachloride and titanium sulfate flocculation in wastewater treatment

Flocculation with titanium tetrachloride (TiCl4) and titanium sulfate (Ti(SO4)2) was investigated in terms of different coagulant doses, pH, turbidity, dissolved organic carbon (DOC), UV-254, colour, zeta potential, particle size and molecular weight distribution. The two coagulants were compared with the commonly used coagulants such as ferric chloride (FeCl3) and aluminium sulfate (Al2(SO 4)3). Titanium tetrachloride showed the highest turbidity removal, while titanium sulfate showed the highest reduction of UV-254 and colour at all pH values. The four coagulants were found to have similar organic removal up to 60-67% and resulted in similar organic removal in terms of various MW ranges. The decantability of the settled flocs was very high for titanium tetrachloride, titanium sulfate and ferric chloride compared with aluminium sulfate. The dominating coagulation mechanisms for titanium tetrachloride and titanium sulfate are still to be studied, since different precipitation reactions might take place at different pH even without flocculant addition. Titanium tetrachloride and titanium sulfate were found as effective new coagulants in wastewater treatment not only in terms of organic matter removal, but also in sludge reduction through the production of titanium dioxide. © IWA Publishing 2009

Photodesorption of specific organic compounds from titanium dioxide particles in aqueous media

This study investigates the photodesorption of organic compounds (beef extract, peptone, humic acid, tannic acid, sodium lignin sulphonate, sodium lauryl sulphate, arabic gum powder and arabic acid) from TiO2 (1 g/L in water, pH 7). After a period to reach adsorption equilibrium, photodesorption experiments were conducted in a recirculated reactor at a constant flow rate of 150 mL/min with a UV light intensity of 24 W. Photodesorption was observed only for sodium lauryl sulphate (50%), sodium lignin sulphonate (43.47%), beef extract (20.35%) and tannic acid (10.5%) indicating that photodesorption is specific to some organic compounds but not to all. Using liquid chromatography-organic carbon detection, untreated beef extract and sodium lignin sulphonate were found to contain significant amounts of humic substances (∼1,000 g/mol), which decreased in concentration after dark phase adsorption, while a significant increase in low molecular weight (<350 g/mol) concentrations was observed after photodesorption. UV-treated sodium lauryl sulphate photodesorbed to give both higher molecular weight (HMW) and lower molecular weight (LMW) organics. Thus, the HMW fractions of organic compounds decomposed into smaller compounds after UV irradiation, which subsequently desorbed from TiO2 surface. However, untreated tannic acid contained a larger proportion of LMW acids, which shows a high adsorption affinity to TiO2 during adsorption and poorly desorbs upon irradiation. © 2013 © 2013 Balaban Desalination Publications. All rights reserved

Viscosity contrasts in the Venus mantle from tidal deformations

The tidal deformations of a planet are often considered as markers of its inner structure. In this work, we use the tide excitations induced by the Sun on Venus for deciphering the nature of its internal layers. In using a Monte Carlo Random Exploration of the space of parameters describing the thickness, density and viscosity of 4 or 5 layer profiles, we were able to select models that can reproduce the observed mass, total moment of inertia, $k_2$ Love number and expected quality factor $Q$. Each model is assumed to have homogeneous layers with constant density, viscosity and rigidity. These models show significant contrasts in the viscosity between the upper mantle and the lower mantle. They also rather favor a S-free core and a slightly hotter lower mantle consistent with previous expectations.Comment: Accepted for publication in Planetary and Space Science

Estudo da eficiência da amostragem descritiva na simulação de um problema de filas

Uma das idéias básicas da simulagção por Monte Carlo consiste no uso da amostragem aleatória simples, reproduzindo assim o comportamento probabilístico de uma variável aleatória. Recentemente, no entanto, foi sugerido um método de amostragem que se considera mais adequado a simulação: a amostragem descritiva. Em essência, a amostragem descritiva baseia-se numa seleção totalmente determinística dos valores amostrais e na sua permutação aleatória. Este trabalho tern por objetivo mostrar, atráves de uma comparação empírica dos dois métodos, a maior eficiência estatística da amostragem descritiva. Para isso, foi estudada a simulção de um problema de filas relativo a descarga de navios em um terminal portuário. Além da comprovação de que a amostragem descritiva conduz a estimativas mais precisas, verificou-se também uma substancial redução do tempo de processamento

Synthesis and characterisation of potassium polytitanate for photocatalytic degradation of crystal violet

© 2014 . Potassium titanate nanostructures were synthesised by hydrothermal treatment of TiO2 (P25) in KOH and H2O2. As-produced powders were characterised by scanning electron microscopy, energy-dispersive X-ray spectroscopy, transmission electron microscopy, X-ray diffraction, and nitrogen adsorption-desorption methods. Longitudinally-oriented-wire-like structures with a length up to several micrometres and diameters ranging from 10 to 30nm were obtained. Larger size fibrous nanowires resulting from the hydrothermal treatment showed high affinity in adsorbing crystal violet (CV), which was mainly due to their high surface area. The photocatalytic bleaching of CV solution revealed that the wires are photoactive under ultraviolet light irradiation. Macroporous nanowires are considered as effective adsorbents of CV, capable of photocatalytic degradation, and they can be easily separated from the solution by settling