Despite the recognized importance of the bond rating industry, little academic work has been done to investigate the determinants of the standards these firms employ to assign credit ratings to individual firms. There is an ongoing debate in the literature arguing whether the decline in the percentage of highly rated firms is because rating standards have become more stringent over time or whether the credit quality of firms in the economy has declined. We investigate this question in this dissertation. Our first contribution is to address several empirical problems in prior literature. This study uses a combination of structural models of default and econometric model of ratings to study the determinants of rating standards and, by doing so, overcome the earlier methodological shortcomings. Our second contribution is to test new theory which hypothesizes that the standards of a rating agency are conditional upon the distribution of default risk in the economy at the time. The results are robust no matter which structural models of default we employ. The evidence suggests the standards are relative to the default risk distribution and there has been a secular increase in the stringency in the assignment of ratings over time. A third way we extend the literature is by examining the accuracy of the assignment of ratings. Theoretical models suggest rating agencies have incentives to purposefully add noise to the assignment of ratings. We conduct an empirical analysis of the classification errors using receiver operating characteristic analysis. The results suggest that error rates have decreased at the extreme ends of the rating spectrum (AAA vs. AA and below; B and below vs. BB and above) over time while it has increased in the middle rating categories. This error rate is directly related to the distribution of default risk across firms at any point in time. These findings not only strengthen our result that standards are relative and time varying, but also suggest there is more noise in the assignment of ratings at exactly the time when there is more uncertainty regarding the credit risk of firms in the economy – i.e., during a credit crisis.

The first chapter is based on a paper with Jin Li in fair division. It was recently discovered that on the domain of Leontief preferences, Hurwicz (1972)'s classic impossibility result does not hold; that is, one can find efficient, strategy-proof and individually rational rules to divide resources among agents. Here we consider the problem of dividing l divisible goods among n agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned. The second and third chapters are based on two working papers of mine in decision making under uncertainty. In the second chapter, I study the wealth effect under uncertainty --- how the wealth level impacts a decision maker's degree of uncertainty aversion. I axiomatize a class of preferences displaying decreasing absolute uncertainty aversion, which allows a decision maker to be more willing to take uncertainty-bearing behavior when he becomes wealthier. Three equivalent preference representations are obtained. The first is a variation on the constraint criterion of Hansen and Sargent (2001). The other two respectively generalize Gilboa and Schmeidler (1989)'s maxmin criterion and Maccheroni, Marinacci and Rustichini (2006)'s variational representation. This class, when restricted to preferences exhibiting constant absolute uncertainty aversion, is exactly Maccheroni, Marinacci and Rustichini (2006)'s ariational preferences. Thus, the results further enable us to establish relationships among the representations for several important classes within variational preferences. The three representations provide different decision rules to rationalize the same class of preferences. The three decision rules correspond to three ways which are proposed in the literature to identify a decision maker's perception about uncertainty and his attitude toward uncertainty. However, I give examples to show that these identifications conflict with each other. It means that there is much freedom in eliciting two unobservable and subjective factors, one's perception about and attitude toward uncertainty, from only his choice behavior. This exactly motivates the work in Chapter 3. In the third chapter, I introduce confidence orders in addition to preference orders. Axioms are imposed on both orders to reveal a decision maker's perception about uncertainty and to characterize the following decision rule. A decision maker evaluates an act based on his aspiration and his confidence in this aspiration. Each act corresponds to a trade-off line between the two criteria: The more he aspires, the less his confidence in achieving the aspiration level. The decision maker ranks an act by the optimal combination of aspiration and confidence on its trade-off line according to an aggregating preference of his over the two-criterion plane. The aggregating preference indicates his uncertainty attitude, while his perception about uncertainty is summarized by a generalized second-order belief over the prior space, and this belief is revealed by his confidence order.

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Statistical models are often used for the prediction of future random variables. There are two types of prediction, point prediction and probabilistic prediction. The prediction accuracy is quantified by performance measures, which are typically based on loss functions. We study the estimators of these performance measures, the prediction error and performance scores, for point and probabilistic predictors, respectively. The focus of this thesis is to assess the prediction performance of survival models that analyze censored survival times. To accommodate censoring, we extend the inverse probability censoring weighting (IPCW) method, thus arbitrary loss functions can be handled. We also develop confidence interval procedures for these performance measures. We compare model-based, apparent loss based and cross-validation estimators of prediction error under model misspecification and variable selection, for absolute relative error loss (in chapter 3) and misclassification error loss (in chapter 4). Simulation results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are often sensitive to model misspecification. The methods are illustrated for two medical contexts in chapter 5. The apparent loss based and cross-validation estimators of performance scores for probabilistic predictor are discussed and illustrated with an example in chapter 6. We also make connections for performance.

Complex number is a major mathematical discovery. It can be used in many scientific fields, including engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory. The aim of this paper investigates the problems of algebra, trigonometry and geometry, which can be solved cleverly by the properties of complex numbers.

The seasonal and diurnal concentrations of atmospheric carbonyls were measured by the LpDNPH-Cartridge and the microcomputer air sampling device at Nan-Chie and Hsiung-Kong sites in Kaohsiung area. Then, factor analysis and absolute principal component analysis were also used to determine the source apportionment in Kaohsiung area. Total concentrations of carbonyls were higher in Summer than in winter at Nan-Chie and Hsiung-Kong sites. Measurements showed that the highest carbonyls were formaldehyde and acetaldehyde, due to the fact that photochemical activities are stronger in summer than in winter. The concentrations of total carbonyls, formaldehyde, acetaldehyde were showed similar diurnal variations, that highest concentrations were found in the morning and noon, then drop down at afternoon and increased at night. Due to the fact that photochemical activities and vehicle exhausts. C1-C3 ratio indicated the local participation of anthropogenic hydrocarbons was important in the production of carbonyls in the Kaohsiung area. C1/C2 was highest in the summer than in the winter, that photochemical activities cause highest concentrations of formaldehyde, especially in the summer noon. The results of factor analysis and absolute principal component analysis showed that the primary pollution sources at Nan-Chie were traffic exhausts (diesel and gasoline vehicle) and stationary sources (petrochemical and food industry) and restaurant emissions, and the primary pollution sources at Hsiung-Kong were traffic exhausts (diesel and gasoline vehicle), stationary emissions (metal assembly and petrochemical industry) and restaurant emissions.

This Thesis attempts to construct a Taiwan equity multi-factor model using fundamental cross-sectional approach step by step. It is found that the model involves 28 explanatory factors (including 20 industry factors) and its explanatory power is 58.6% on average. The results of the estimations can be considered very satisfactory. Moreover, based on MFM, this study simulates applications of equity market neutral strategies through quantitative techniques over the period Jan.2003 ¡V Dec.2003. The results verified that the three major characteristics of equity market neutral portfolio performance are: 1) providing absolute return; 2) lack of correlation to the equity benchmark; and 3) low volatility due to hedged portfolio structures.

LCModel has been widely used for MR spectroscopy analysis. LCMgui, which is the built-in user interface of LCModel, based on Linux system, provides the functionality to convert MRS data of various formats to match the format of LCModel raw file, except for GE MRSI data which can be analyzed by LCModel only with GE Sage/IDL software. Hence, the first part of this work was to develop a multi-platform tool with LCModel to support all GE data, including GE MRSI data and phased array data. With this tool, users can analyze MRS data with LCModel on their familiar environment such as Windows, and Linux. The MR spectroscopy experiments with phased array coils provide optimized SNR which lead to more accurate absolute quantification by some sophisticate combination algorithms of phased array coils. Thus, the second part of this work was to propose an algorithm of combining data obtained from phased array coils by doing phase correction and calculation of weighting factor. In addition, the comparison of the accuracy between using quadrature coil and phased array coils with different combination algorithms was investigated in order to demonstrate the efficiency of using phased array coils and the combination program.

<p>In this thesis we apply linear feedback control to spatially evolving flows in order to minimize disturbance growth. The dynamics is assumed to be described by the linearized Navier--Stokes equations. Actuators and sensor are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier--Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier--Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. One possible approach is to perform Fourier decomposition along (almost) homogeneous spatial directions and another is by constructing a reduced order model by Galerkin projection on a suitable set of vectors. The first strategy is used to control the evolution of a range of instabilities in the classical family of Falkner--Skan--Cooke flows whereas the second is applied to a more complex cavity type of geometry.</p>

Texte remanié de : Habilitationsschrift : Philosophie, Pädagogik und Publizistik : Ruhr-Universität Bochum : 2004. / Bibliogr. p. [525]-556.