Lau, Ka Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 46-48). / Abstract also in Chinese. / Chapter 1 --- Introduction to Global Credit Risk Management Standard --- p.1 / Chapter 1.1 --- Background --- p.2 / Chapter 1.2 --- Basel Accords --- p.2 / Chapter 1.3 --- Risk Bucketing --- p.7 / Chapter 2 --- Current Practices of Risk Bucketing and PD Estimation --- p.10 / Chapter 2.1 --- Credit Scoring --- p.10 / Chapter 2.2 --- Risk Bucketing after Credit Scoring --- p.12 / Chapter 2.3 --- Related Literature Review --- p.14 / Chapter 2.4 --- Objective --- p.16 / Chapter 3 --- Bayesian Model for risk bucketing --- p.17 / Chapter 3.1 --- The Model --- p.17 / Chapter 3.2 --- Posterior Distribution --- p.19 / Chapter 3.3 --- Gibbs Sampler for the Posterior Distribution --- p.22 / Chapter 3.3.1 --- General Gibbs Sampler Theory --- p.22 / Chapter 3.3.2 --- The Gibbs Sampler for the Proposed Model --- p.23 / Chapter 3.4 --- Monitoring Convergence of the Gibbs Sampler --- p.26 / Chapter 3.5 --- "Estimation, Bucketing and Prediction" --- p.28 / Chapter 3.5.1 --- Estimation --- p.28 / Chapter 3.5.2 --- Bucketing --- p.28 / Chapter 3.5.3 --- Prediction --- p.29 / Appendix --- p.29 / Chapter 4 --- Simulation Studies and Real Data Analysis --- p.32 / Chapter 4.1 --- Simulation Studies --- p.32 / Chapter 4.1.1 --- Details of Simulation --- p.32 / Chapter 4.1.2 --- Simulation Procedures --- p.34 / Chapter 4.1.3 --- Predictive Performance --- p.35 / Chapter 4.1.4 --- Summary of Simulation Results --- p.36 / Chapter 4.2 --- Real Data Analysis --- p.37 / Chapter 5 --- Conclusion and Discussion --- p.44 / Bibliography --- p.46

[Truncated abstract] This thesis presents an operationally applicable and reliable model for quantification of the exposure of underground mining personnel to geotechnical hazards. The model is shown to have the flexibility to apply to very different operational environments, within the context of mechanised metalliferous mines. It provides an essential component for carrying out quantitative geotechnical risk analyses of underground mines. Increasingly prevalent within the Australian mining industry are moves towards a riskbased philosophy instead of prescriptive design procedures. A barrier to this has been the lag in availability of resources (personnel and technical) required for the intensive effort of applying probabilistic methods to geotechnical engineering at mines ... One of the missing components for quantitative risk analysis in mines has been an accurate model of personnel exposure to geotechnical hazards, from which meaningful estimates can be made of the probabilities of serious or fatal injury given a rockfall. Exposure profiling for geotechnical risk analysis at minesites has traditionally involved the simple classification of travelways and entry areas by their occupancy rate, not taking into account traffic and work characteristics which may significantly influence the risks. Therefore, it was the focus of this thesis to address that deficiency and progress the ability to perform semi-quantitative and quantitative risk analyses in mines.

In this thesis we consider two comparative statics questions of changes in risk. The first question concerns situations where an individual faces some risk and has no control over the uncertain environment. In these situations we ask what kind of changes in risk will cause the individual's expected utility to increase. The second comparative statics question concerns situations where an individual faces some risk and has some control over the uncertain environment. In particular, we consider situations where the individual maximizes her expected utility with respect to some control parameter. Here we ask what kind of changes in risk will cause the individual's optimal value of the control parameter to increase. The existing literature has answered these questions for a class of individuals (for example, the class of risk averse individuals). This thesis differs from existing literature as it focuses on a given individual, and thus reveals some of the person-specific factors that affect individual?s responses to changes in risk. The aim of the thesis is to show how an order on distributions, termed single crossing likelihood ratio (SCLR) order, can intuitively answer both questions for a given individual. The main contributions of the thesis are as follows. First, the thesis presents the SCLR order and its main properties. Second, the thesis shows that the SCLR order can answer the above comparative statics questions in an intuitive way. In particular, the thesis shows that the answer to the above questions, with the use of the SCLR order, depends on a risk reference point which can be interpreted as a "certainty equivalent" point. Thus it is demonstrated that individual's responses to changes in risk are affected by her "certainty equivalent" point. Lastly, the results of the thesis can be used to provide an intuitive explanation of related existing results that were obtained for a class of individuals.

In this thesis we consider two comparative statics questions of changes in risk. The first question concerns situations where an individual faces some risk and has no control over the uncertain environment. In these situations we ask what kind of changes in risk will cause the individual's expected utility to increase. The second comparative statics question concerns situations where an individual faces some risk and has some control over the uncertain environment. In particular, we consider situations where the individual maximizes her expected utility with respect to some control parameter. Here we ask what kind of changes in risk will cause the individual's optimal value of the control parameter to increase. The existing literature has answered these questions for a class of individuals (for example, the class of risk averse individuals). This thesis differs from existing literature as it focuses on a given individual, and thus reveals some of the person-specific factors that affect individual?s responses to changes in risk. The aim of the thesis is to show how an order on distributions, termed single crossing likelihood ratio (SCLR) order, can intuitively answer both questions for a given individual. The main contributions of the thesis are as follows. First, the thesis presents the SCLR order and its main properties. Second, the thesis shows that the SCLR order can answer the above comparative statics questions in an intuitive way. In particular, the thesis shows that the answer to the above questions, with the use of the SCLR order, depends on a risk reference point which can be interpreted as a "certainty equivalent" point. Thus it is demonstrated that individual's responses to changes in risk are affected by her "certainty equivalent" point. Lastly, the results of the thesis can be used to provide an intuitive explanation of related existing results that were obtained for a class of individuals.

Thesis (PhD (Statistics and Actuarial Sciences))--Stellenbosch University, 2008. / We consider the problem of model assessment by risk estimation. Various approaches to risk estimation are considered in a uni ed framework. This a discussion of various complexity dimensions and approaches to obtaining bounds on covering numbers is also presented. The second type of training sample interval estimator discussed in the thesis is Rademacher bounds. These bounds use advanced concentration inequalities, so a chapter discussing such inequalities is provided. Our discussion of Rademacher bounds leads to the presentation of an alternative, slightly stronger, form of the core result used for deriving local Rademacher bounds, by avoiding a few unnecessary relaxations. Next, we turn to a discussion of PAC-Bayesian bounds. Using an approach developed by Olivier Catoni, we develop new PAC-Bayesian bounds based on results underlying Hoe ding's inequality. By utilizing Catoni's concept of \exchangeable priors", these results allowed the extension of a covering number-based result to averaging classi ers, as well as its corresponding algorithm- and data-dependent result. The last contribution of the thesis is the development of a more exible shell decomposition bound: by using Hoe ding's tail inequality rather than Hoe ding's relative entropy inequality, we extended the bound to general loss functions, allowed the use of an arbitrary number of bins, and introduced between-bin and within-bin \priors". Finally, to illustrate the calculation of these bounds, we applied some of them to the UCI spam classi cation problem, using decision trees and boosted stumps. framework is an extension of a decision-theoretic framework proposed by David Haussler. Point and interval estimation based on test samples and training samples is discussed, with interval estimators being classi ed based on the measure of deviation they attempt to bound. The main contribution of this thesis is in the realm of training sample interval estimators, particularly covering number-based and PAC-Bayesian interval estimators. The thesis discusses a number of approaches to obtaining such estimators. The rst type of training sample interval estimator to receive attention is estimators based on classical covering number arguments. A number of these estimators were generalized in various directions. Typical generalizations included: extension of results from misclassi cation loss to other loss functions; extending results to allow arbitrary ghost sample size; extending results to allow arbitrary scale in the relevant covering numbers; and extending results to allow arbitrary choice of in the use of symmetrization lemmas. These extensions were applied to covering number-based estimators for various measures of deviation, as well as for the special cases of misclassi - cation loss estimators, realizable case estimators, and margin bounds. Extended results were also provided for strati cation by (algorithm- and datadependent) complexity of the decision class. In order to facilitate application of these covering number-based bounds,

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Accurate estimation of Value at Risk (VaR) and Expected Shortfall (ES) is critical in the management of extreme market risks. These risks occur with small probability, but the financial impacts could be large. Traditional models to estimate VaR and ES are investigated. Following usual practice, 99% 10 day VaR and ES measures are calculated. A comprehensive theoretical background is first provided and then the models are applied to the Africa Financials Index from 29/01/1996 to 30/04/2013. The models considered include independent, identically distributed (i.i.d.) models and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) stochastic volatility models. Extreme Value Theory (EVT) models that focus especially on extreme market returns are also investigated. For this, the Peaks Over Threshold (POT) approach to EVT is followed. For the calculation of VaR, various scaling methods from one day to ten days are considered and their performance evaluated. The GARCH models fail to converge during periods of extreme returns. During these periods, EVT forecast results may be used. As a novel approach, this study considers the augmentation of the GARCH models with EVT forecasts. The two-step procedure of pre-filtering with a GARCH model and then applying EVT, as suggested by McNeil (1999), is also investigated. This study identifies some of the practical issues in model fitting. It is shown that no single forecasting model is universally optimal and the choice will depend on the nature of the data. For this data series, the best approach was to augment the GARCH stochastic volatility models with EVT forecasts during periods where the first do not converge. Model performance is judged by the actual number of VaR and ES violations compared to the expected number. The expected number is taken as the number of return observations over the entire sample period, multiplied by 0.01 for 99% VaR and ES calculations. / AFRIKAANSE OPSOMMING: Akkurate beraming van Waarde op Risiko (Value at Risk) en Verwagte Tekort (Expected Shortfall) is krities vir die bestuur van ekstreme mark risiko’s. Hierdie risiko’s kom met klein waarskynlikheid voor, maar die finansiële impakte is potensieel groot. Tradisionele modelle om Waarde op Risiko en Verwagte Tekort te beraam, word ondersoek. In ooreenstemming met die algemene praktyk, word 99% 10 dag maatstawwe bereken. ‘n Omvattende teoretiese agtergrond word eers gegee en daarna word die modelle toegepas op die Africa Financials Index vanaf 29/01/1996 tot 30/04/2013. Die modelle wat oorweeg word sluit onafhanklike, identies verdeelde modelle en Veralgemeende Auto-regressiewe Voorwaardelike Heteroskedastiese (GARCH) stogastiese volatiliteitsmodelle in. Ekstreemwaarde Teorie modelle, wat spesifiek op ekstreme mark opbrengste fokus, word ook ondersoek. In hierdie verband word die Peaks Over Threshold (POT) benadering tot Ekstreemwaarde Teorie gevolg. Vir die berekening van Waarde op Risiko word verskillende skaleringsmetodes van een dag na tien dae oorweeg en die prestasie van elk word ge-evalueer. Die GARCH modelle konvergeer nie gedurende tydperke van ekstreme opbrengste nie. Gedurende hierdie tydperke, kan Ekstreemwaarde Teorie modelle gebruik word. As ‘n nuwe benadering oorweeg hierdie studie die aanvulling van die GARCH modelle met Ekstreemwaarde Teorie vooruitskattings. Die sogenaamde twee-stap prosedure wat voor-af filtrering met ‘n GARCH model behels, gevolg deur die toepassing van Ekstreemwaarde Teorie (soos voorgestel deur McNeil, 1999), word ook ondersoek. Hierdie studie identifiseer sommige van die praktiese probleme in model passing. Daar word gewys dat geen enkele vooruistkattingsmodel universeel optimaal is nie en die keuse van die model hang af van die aard van die data. Die beste benadering vir die data reeks wat in hierdie studie gebruik word, was om die GARCH stogastiese volatiliteitsmodelle met Ekstreemwaarde Teorie vooruitskattings aan te vul waar die voorafgenoemde nie konvergeer nie. Die prestasie van die modelle word beoordeel deur die werklike aantal Waarde op Risiko en Verwagte Tekort oortredings met die verwagte aantal te vergelyk. Die verwagte aantal word geneem as die aantal obrengste waargeneem oor die hele steekproefperiode, vermenigvuldig met 0.01 vir die 99% Waarde op Risiko en Verwagte Tekort berekeninge.

Fu Gang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 71-72). / Abstracts in English and Chinese. / ABSTRACT OF THESIS ENTITLED --- p.I / ACKNOWLEDGEMENT --- p.III / TABLE OF CONTENT --- p.IV / LIST OF FIGURES --- p.VII / LIST OF TABLES --- p.VIII / Chapter CHAPTER 1 --- INTRODUCTION --- p.1 / Chapter 1.1 --- A Third-party E-commerce Logistics Center in Need --- p.1 / Chapter 1.2 --- Difficulty in Designing the Logistics Center --- p.2 / Chapter 1.3 --- AHP and ANP --- p.3 / Chapter 1.4 --- Scope of the Study --- p.4 / Chapter 1.5 --- Organization of the Thesis --- p.5 / Chapter CHAPTER 2 --- BACKGROUND AND LITERATURE REVIEW --- p.7 / Chapter 2.1 --- Third-party E-commerce Logistics Center --- p.7 / Chapter 2.2 --- "Government, Investors, and Users" --- p.8 / Chapter 2.3 --- Center Design --- p.11 / Chapter 2.3.1 --- Information and Physical Infrastructure --- p.11 / Chapter 2.3.2 --- Ownership Arrangement --- p.12 / Chapter 2.3.3 --- Design Alternatives --- p.13 / Chapter 2.4 --- Evaluating Design Alternatives --- p.17 / Chapter CHAPTER 3 --- AHP MODEL --- p.19 / Chapter 3.1 --- Introduction of AHP --- p.19 / Chapter 3.2 --- AHP Models for Government --- p.20 / Chapter 3.2.1 --- Benefit to Government --- p.20 / Chapter 3.2.2 --- Cost to Government --- p.23 / Chapter 3.2.3 --- Risk to Government --- p.24 / Chapter 3.3 --- AHP Models for Investors --- p.25 / Chapter 3.3.1 --- Benefit to Investors --- p.25 / Chapter 3.3.2 --- Cost to Investors --- p.28 / Chapter 3.3.3 --- Risk to Investors --- p.29 / Chapter 3.4 --- AHP Models for Users --- p.32 / Chapter 3.4.1 --- Benefit to Users --- p.32 / Chapter 3.4.2 --- Cost to Users --- p.34 / Chapter 3.4.3 --- Risk to Users --- p.36 / Chapter CHAPTER 4 --- RISK SHARING IN CENTER DESIGN ´ؤ USING AHP MODEL --- p.38 / Chapter 4.1 --- "Solution Methodology of Aggregating Benefit, Cost and Risk in AHP" --- p.38 / Chapter 4.2 --- Aspects in Determining an Agreeable Solution --- p.40 / Chapter 4.3 --- Sensitivity Analysis in AHP --- p.42 / Chapter 4.4 --- A Conflict-Resolving Solution Procedure for AHP --- p.44 / Chapter 4.5 --- An Illustrative Numerical Example in AHP --- p.48 / Chapter CHAPTER 5 --- ANP MODEL --- p.51 / Chapter 5.1 --- Introduction of ANP --- p.51 / Chapter 5.2 --- ANP Models for Government --- p.53 / Chapter 5.2.1. --- Benefit to Government --- p.55 / Chapter 5.2.2. --- Cost to Government --- p.54 / Chapter 5.2.3. --- Risk to Government --- p.54 / Chapter 5.3 --- ANP Models for Investors --- p.56 / Chapter 5.3.1 --- Benefit to Investors --- p.56 / Chapter 5.3.2 --- Cost to Investors --- p.56 / Chapter 5.3.3 --- Risk to Investors --- p.56 / Chapter 5.4 --- ANP Models for Users --- p.56 / Chapter 5.4.1 --- Benefit to Users --- p.56 / Chapter 5.4.2 --- Cost to Users --- p.58 / Chapter 5.4.3 --- Risk to Users --- p.58 / Chapter CHAPTER 6 --- RISK SHARING IN CENTER DESIGN ´ؤ USING ANP MODEL --- p.60 / Chapter 6.1 --- Aggregated Benefit-Cost-Risk ANP Model --- p.60 / Chapter 6.2 --- Sensitivity Analysis of ANP Model in an AHP Fashion --- p.61 / Chapter 6.3 --- Sensitivity Analysis of General ANP Model --- p.62 / Chapter 6.4 --- A Conflict-Resolving Solution Procedure for ANP --- p.63 / Chapter 6.5 --- An Illustrative Numerical Example in ANP --- p.66 / Chapter CHAPTER 7 --- p.69 / CONCLUSION --- p.69 / BIBLIOGRAPHY --- p.71