Measuring the risk of a credit portfolio is a challenge for financial institutions because of the regulations brought by the Basel Committee. In recent years lots of models and state-of-the-art methods, which utilize Monte Carlo simulation, were proposed to solve this problem. In most of the models factors are used to account for the correlations between obligors. We concentrate on the the normal copula model, which assumes multivariate normality of the factors. Computation of value at risk (VaR) and expected shortfall (ES) for realistic credit portfolio models is subtle, since, (i) there is dependency throughout the portfolio; (ii) an efficient method is required to compute tail loss probabilities and conditional expectations at multiple points simultaneously. This is why Monte Carlo simulation must be improved by variance reduction techniques such as importance sampling (IS). Thus a new method is developed for simulating tail loss probabilities and conditional expectations for a standard credit risk portfolio. The new method is an integration of IS with inner replications using geometric shortcut for dependent obligors in a normal copula framework. Numerical results show that the new method is better than naive simulation for computing tail loss probabilities and conditional expectations at a single x and VaR value. Finally, it is shown that compared to the standard t statistic a skewness-correction method of Peter Hall is a simple and more accurate alternative for constructing confidence intervals. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Šio darbo tikslas – ištirti stochastinio programavimo energetikos uždavinį. Darbe tyrinėta Lietuvos energetikos struktūra, taip pat tyrinėti optimizavimo metodai. Sudarytas Lietuvos energetikos uždavinio modelis. Optimizavimo modelis realizuotas Java programa. Optimizavimo programoje panaudotos objektinio ir lygiagretaus programavimo paradigmos. Atlikti energetikos uždavinio parametrų tyrimai. / Primary goal of this work was to research stochastic programming model of the energetic system. In this paper we also studied Lithuanian energetic sector structure and made Lithuanian energetic model. This model was realized in Java programming language. Created program is written using object-oriented and parallel programming paradigms. Also we researched different parameters influence on the model.

This work describes the installation of a Beowulf cluster at the University of KwaZulu-Natal / Thesis (Ph.D.-Eng)-University of KwaZulu-Natal, 2006.

Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica. / Department of Mathematical Sciences

Calculations of the electronic properties of AIN, GaN, InN and their alloys are presented. Initial calculations are performed using the first principles pseudopotenial method to obtain accurate lattice constants. Further calculations then investigate bonding in the nitrides through population analysis and density of state calculations, the empirical pseudopotential method is also used in this work. Pseudopotentials 'or each of the nitrides are constructed using a functional form that allows strained material and alloys to be studied. The conventional k,p valence band parameters for both zincblende and wurtzite are obtained from the empirical band structure using two different methods. A Monte-Carlo fitting of the k.p band structure to the pseudopotential data (or an effective mass method for the zincblende structure) is used to produce one set. Another set is obtained directly from the momentum matrix elements and energy eigenvalues at the centre of the Brillouin zone. Both methods of calculating k.p parameters produce band structure in excellent agreement with the original empirical band calculations near the centre of the Brillouin zone. The advantage of the direct method is that it produces consistent sets of parameters, and can be used in studies involving a series of alloy compositions. Further empirical pseudopotential method calculations are then performed for alloys of the nitrides. In particular, the variation of the band gap with alloy composition is investigated, and good agreement with theory and experiment is found. The direct method is used to obtain k.p parameters for the alloys, and is contrasted with the fitting approach. The behaviour of the nitrides under strain is also studied. In particular, valence band offsets for nitride heterojunctions are calculated, and a strong forward-backward asymmetry in the band offset is found, in good agreement with other results in the literature.

Many contemporary experimental QCD results achieve greater accuracy in measurement than equivalent theoretical predictions calculated at leading order. Therefore it is necessary to consider next to leading order (NLO) predictions for many processes in order to compare experiment with theory. Accurate theoretical predictions are also important in order to reduce the uncertainty in QCD parameters such as the coupling constant a, and to test whether QCD is in fact the correct theory to describe the strong interaction. With NLO results it is also possible to separate different clustering algorithms and test non-perturbative effects. This thesis concentrates on the techniques necessary for the calculation of NLO observables from the processes e(^+)e(^-) → 4 jets and pp → γ + X. We formulate a new version of the hybrid subtraction scheme based on the colour antenna structure of the final state to evaluate the necessary phase space integrals for the 4 jet process. The scheme is universal and can be applied to any QCD processes. The general purpose Monte Carlo EERAD2 which incorporates this new technique is compared with both experimental data gathered by the DELPHI collaboration and other groups which have reported similar calculations. A Monte Carlo written for the process pp → γ + X requires a knowledge of the non- perturbative photon fragmentation function, D(_γ), and the second half of this thesis concentrates on a calculation of this process using the ALEPH measurement of D(_γ) based on a democratic algorithm. The Monte Carlo DPRAD incorporates these techniques and results from it are compared with data from the Tevatron.

No description available.

The scope of this study is to estimate the zero-coupon yield curve of tomorrow by using Vasicek yield curve model with the zero-coupon bond yield data of today. The raw data of this study is the yearly simple spot rates of the Turkish zero-coupon bonds with different maturities of each day from July 1, 1999 to March 17, 2004. We completed the missing data by using Nelson-Siegel yield curve model and we estimated tomorrow yield cuve with the discretized Vasicek yield curve model.

In the last decade, ultracold plasmas have been created in the laboratory by photo-ionizing laser-cooled atoms. To understand the overall dynamics of ultracold plasmas, one needs to understand Rydberg collisional processes at ultracold temperatures. The two kinds of problems addressed in this thesis are: study of Rydberg atomic processes at ultracold temperatures, and a study of the overall dynamics of the ultracold plasmas. Theoretical methods based on quantal-classical correspondence is used to understand Rydberg atomic processes such as radiative cascade, and radiative recombination. A simulation method suitable for ultracold collisions is developed and tested. This method is then applied to study collisional-Stark mixing in Rydberg atoms. To study the dynamics of the ultracold plasmas, a King model for the electrons in plasmas is proposed. The King model is a stationary, finite sized electron distribution for the electrons in a cloud of fixed ions with a Gaussian distribution. A Monte-Carlo method is developed to simulate the overall dynamics of the King distribution.

Improving computer technology and the desire to more accurately model the heterogeneity of the nuclear reactor environment have made the use of Monte Carlo depletion codes more attractive in recent years, and feasible (if not practical) even for 3-D depletion simulation. However, in this case statistical uncertainty is combined with error propagating through the calculation from previous steps. In an effort to understand this error propagation, four test problems were developed to test error propagation in the fuel assembly and core domains. Three test cases modeled and tracked individual fuel pins in four 17x17 PWR fuel assemblies. A fourth problem modeled a well-characterized 330MWe nuclear reactor core. By changing the code's initial random number seed, the data produced by a series of 19 replica runs of each test case was used to investigate the true and apparent variance in k-eff, pin powers, and number densities of several isotopes. While this study does not intend to develop a predictive model for error propagation, it is hoped that its results can help to identify some common regularities in the behavior of uncertainty in several key parameters.