M.Sc., Faculty of Science, University of the Witwatersrand, 2011 / Existing water management initiatives, strategies and policies in South Africa, ranging from the overarching water management legislative framework to the local-level practical operational aspects, were examined as a component of this project. The integration between National Strategies pertaining to water resource management and local implementation was addressed in terms of examining Water Conservation and Demand Management approaches and assessing the effectiveness of these approaches in addressing climate change risk factors in the water sector. Current South African regulatory instruments in the water sector allow adaptation and flexibility in order to address climate change impacts on the water resources in South Africa. The greatest obstacle in the implementation of effective Integrated Water Resource Management (IWRM) for climate change adaptation strategies is the lack of institutional support required from national levels of government to local municipalities. There is also a lack of strategic guidance and support in the form of policies specific to climate risk in the water sector in South Africa. Another important aspect of the IWRM, namely social learning, also suffers in the process due to lack of participation from key stakeholders and limited integration amongst interdependent sectors.

A Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy 2015. / Gold mining in South Africa has been the backbone of the economy for many years. With it came economic well-being, the growth and development of satellite towns, cities and metropolitan cities, e.g. Johannesburg-a place of gold. Unfortunately, it also came with adverse effects, most of which are now evident, after a century of mining, with little or no regard for pollution prevention or any form of remediation. Of interest, in this study, is the presence of tailings storage facilities (TSFs) found within the residential areas, in close proximity to commercial district and industry, having been built around them. Currently, some 270 TSFs lie dormant, pregnant with vast number of toxic heavy metals from the initially low efficient but selective gold processing techniques. This led to the deposition of the sand dumps, with high sulphur, iron, chromium, cadmium, arsenic, and mercury amongst other toxic metals. Exposure to oxygen, and water, the pyrites were oxidized and formed acid mine drainage (AMD), which resulted in the leaching out all toxic heavy metals into ground water and surface water causing serious water pollution and environmental degradation. Due to the low efficient gold processing technique, some gold amount was discarded together with the tailings materials. The reprocessing of these dumps led to the generation of dust, which is easily distributed over large areas of land. The unrehabilitated, semi-rehabilitated, and the abandoned TSFs contributed to all forms of pollution, majorly, windblown dust from unprotected tops and sides, AMD leaching toxic heavy metals. In this study, mercury, one of the most toxic elements found within the vast TSFs was determined. This was carried out as part of a larger environmental impact assessment on the effects and scale of pollution from the gold mining in the Witwatersrand. The study area consisted of the greater Johannesburg area, covering commercial business district (CBD), the industrial areas (Aeroton, City Deep, Germiston, Selby, Springs), and the residential areas (Alberton, Boksburg, Centurion, Germiston, Greenside, Sandton, Springs). Dust samples were collected from paved surfaces in the streets, and accessible buildings, were sieved into three sieved into three fractions (PM100, PM50, PM25), and most of the work focused on the smallest size fraction (PM25) in order to study impact of inhalable and respirable dust. Three sequential extraction procedures (modified BCR-the European Community Bureau of Reference, selective sequential procedure (SSE), and novel sequential extraction procedure (n-SEP)) were applied for partitioning and evaluating the mobility, availability and persistence of mercury in urban dusts. Bioavailability of mercury was assessed by leaching dust with artificial gastric and lung fluids which mimicked body conditions. Contamination levels were assessed based on the enrichment factor (EF), contamination factor (Cf) and geoaccumulation index (Igeo) were calculated to further assess the environmental risk and provide a preliminary estimate of the main sources of mercury in street dust. Non-carcinogenic effects and carcinogenic effects due to exposure to urban street dusts were assessed for both children and adults. The total mercury (HgTOT) ranged from 269 to 1350 μg kg-1. In the PM25 size fraction, mercury exhibited the following decreasing order of HgTOT: industrial area > CBD > residential area. This order shows that the HgTOT concentration in the street dust decreased with increased distance from the TSFs. The highlight was that the highest HgTOT was reported in industrial areas next to the TSFs, tailings reprocessing areas, and tailings footprints. Furthermore, in residential areas grossly affected by TSFs and tailings reprocessing, reported high HgTOT values similar to those reported for industrial samples. These results indicated that the presence of TSFs were largely responsible for the mercury found in the dust. The results from the characterization of the dust showed a large concentration of fine particulate matter, with the characteristically high quartz (74 – 98 wt. %), and minor minerals phases such as chloritoid, chlorite, K-feldspar, jarosite, mica, muscovite, pyrite, and pyrophyllite, all below 10 wt. %. These have been known to enrich trace metals, hence a high concentration of mercury. The close proximity of the tailings to the communities led to the determination of bioavailability of mercury from dust. The bioaccessible Hg extracted by lung fluid (up to 3% of HgTOT) was higher than that of gastric fluid (up to 1% of HgTOT) and was related to the mobile pool of Hg in dust. This suggests that human exposure to Hg in dust via inhalation is greater than that via the gastric tract. These values were very similar to the values obtained from water soluble phase in the sequential extraction procedure (average 1.4% of HgTOT). This indicated that these fluids were able to extract the most bioavailable fraction of Hg, which is responsible for most of the transformation reactions involving mercury. Contamination assessment factor was carried out to classify the pollution levels and indicate whether they are from natural or anthropogenic sources. Based on the EF, Cf, and Igeo, 70, 82, and 84% of the street dust samples were classified as heavily enriched, very highly contaminated, and strongly polluted by mercury, respectively, indicating that they are of anthropogenic origin. The human health risk model was useful in identifying the areas of health risks from exposure to mercury pollution. It showed that children were more vulnerable than adults when exposed to mercury in dust via ingestion. The cancer risk for exposure to As, Cd, and Cr by both children and adults was significantly high for oral ingestion of dust. Cr (VI) was the highest contributor followed by As and lastly Cd. For inhalation pathway, the possibility of developing cancer after a lifetime exposure was low and below the acceptable limits (10-6).

No / Risk assessment is a strategic approach for building resilient supply chains in different types of industries, including the energy sector. In case of an important event with a high level of the risk happening, it could jeopardize the operations of an organization. This could even interrupt the delivery of a product or service, damaging the profitability and reputation of the organization. This could also have a long-term effect on the strategic performance of the firm. Furthermore, key risks might be linked through causal interrelationships. Given the nature of a dynamic business environment, risk assessment also needs to consider the effect of time on those risks. Hence, it is important to understand the behaviour of a complex and dynamic system of interrelated risks to improve strategic decision making in the energy sector. This paper presents a System Dynamics model to assess risks with a supply chain perspective for power plants. The risk assessment model was validated with a case study of three power plants in the Middle East. The developed risk assessment model allowed to understand the long-term effect of risk on three performance indicators: availability of the power plant, efficiency, and operational and maintenance costs. The model provides a different approach to traditional risk assessment by proposing a dynamic modelling methodology.

by Chan Pui Man. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 108-111). / ABSTRACT --- p.II / TABLE OF CONTENTS --- p.III / ACKNOWLEDGEMENT --- p.VI / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- LITERATURE REVIEW --- p.4 / Impact due to Deregulation --- p.5 / Impact due to Globalization --- p.5 / Impact due to Securitization --- p.6 / Impact due to Institutionalisation --- p.6 / Impact due to Computerisation --- p.7 / Chapter III. --- CONCEPT: MANAGEMENT OF RISK --- p.8 / Definition of Risk --- p.9 / Risk Analysis --- p.10 / Risk Assessment --- p.10 / Risk Measurement --- p.10 / Risk Management --- p.11 / Chapter IV. --- TYPE OF RISK --- p.13 / Market/Capital Risk --- p.14 / Reinvestment Risk --- p.15 / Interest Rate Risk --- p.16 / Credit Risk --- p.17 / Liquidity or Funding Risk --- p.18 / Currency and Foreign Exchange Risk --- p.19 / Inflation Risk --- p.19 / Operations Risk --- p.20 / Legal Risk --- p.20 / Political Risk --- p.21 / Systemic Risk --- p.22 / Portfolio Risk --- p.22 / Control Risk --- p.23 / Settlement Risk --- p.23 / Country Risk --- p.24 / Underwriting Risk --- p.24 / Residual or Moral Risk --- p.24 / Strategy Risk and Environment Risk --- p.25 / Chapter V. --- MEASURING CHANGING RISK --- p.26 / Historical Estimates --- p.28 / Non-parametric Methods --- p.29 / Parametric Methods --- p.30 / Chapter VI. --- EVOLUTION OF RISK ESTIMATION --- p.35 / Chapter VII. --- APPLYING PORTFOLIO THEORY INTO RISK ANALYSIS --- p.41 / Modelling Bank Risk --- p.43 / Identification of linkages between an individual loan and bank's overall risk profile --- p.43 / Distribution of expected values --- p.44 / Portfolio expected value --- p.44 / Scenario Analysis and Formation of Loan Risk Measurement --- p.45 / Subsystem --- p.45 / Formation of an Integrated Risk Measurement --- p.45 / Active Management of Portfolio Risk --- p.49 / Chapter VIII. --- RISK ANALYSIS OF INTERNATIONAL INVESTMENT --- p.51 / Discounted-Cash-Flow Analysis --- p.51 / Net Present Value Approach --- p.51 / Internal Rate of Return Approach --- p.54 / Break-even Probability Analysis --- p.55 / Certainty-Equivalent Method --- p.56 / Chapter IX. --- CONSTRUCTING A MODEL FOR RISK ASSESSMENT --- p.58 / "Set up a Model to Estimate ""Capital at Risk""" --- p.58 / Obey the Minimum Standards --- p.60 / Audit and Verify the Model --- p.62 / Chapter X. --- METHODOLOGIES OF RISK MEASUREMENT / Measuring Market Risk : J P Morgan Risk Management Methodology - RiskMetrics´ёØ --- p.64 / Statistical Analysis of Returns and Risk --- p.66 / Market Moves and Locally Gaussian Processes --- p.72 / Stochastic Volatility --- p.72 / Risk and Optionality --- p.73 / Mapping and Term Structure of Interest Rates --- p.73 / Measuring Position Risk --- p.75 / The Simplified Portfolio Approach --- p.77 / The Comprehensive Approach --- p.81 / The Building-Block Approach --- p.83 / Chapter XI. --- ITEMS INVOLVED IN RISK MANAGEMENT --- p.85 / Management Control --- p.35 / Constructing Valuation Methodology --- p.90 / Contents of Reporting --- p.92 / Evaluation of Risk --- p.93 / Counterparty Relationships --- p.93 / Chapter XII. --- AFTERTHOUGHT --- p.95 / APPENDIX --- p.98 / BIBLIOGRAPHY --- p.108

本论文主要研究两类风险估计问题：一类是美式期权价格关于模型参数的敏感性估计， 另一类是投资组合的风险估计。针对这两类问题，我们相应地提出了高效的蒙特卡洛模拟方法。这构成了本文的两个主要部分。 / 第二章是本文的第一部分。在这章中，我们将美式期权的敏感性估计问题提成了更具一般性的估计问题：如果一个随机最优化问题依赖于某些模型参数， 我们该如何估计其最优目标函数关于参数的敏感性。在该问题中， 由于最优决策关于模型参数可能不连续，传统的无穷小扰动分析方法不能直接应用。针对这个困难，我们提出了一种广义的无穷小扰动分析方法，得到敏感性的无偏估计。 我们的方法显示, 在估计敏感性时， 其实并不需要样本路径关于参数的可微性。这是我们在理论上的新发现。另一方面， 该方法可以非常容易的应用于美式期权的敏感性估计。在实际应用中敏感性的无偏估计可以直接嵌入流行的美式期权定价算法，从而同时得到期权价格和价格关于模型参数的敏感性。包括高维问题和多种不同的随机过程模型在内的数值实验， 均显示该估计在计算上具有显著的优越性。最后，我们还从理论上刻画了美式期权的近似最优执行策略对敏感性估计的影响，给出了误差上界。 / 第三章是本文的第二部分。在本章中，我们研究投资组合的风险估计问题。该问题也可被推广成一个一般性的估计问题：如何估计条件期望在作用上一个非线性泛函之后的期望。针对该类估计问题，我们提出了一种多层模拟方法。我们的估计量实际上是一些简单嵌套估计量的线性组合。我们的方法非常容易实现，并且可以被广泛应用于不同的问题结构。理论分析表明我们的方法适用于不同维度的问题并且算法复杂性低于文献中现有的方法。包括低维和高维的数值实验验证了我们的理论分析。 / This dissertation mainly consists of two parts: a generalized infinitesimal perturbation analysis (IPA) approach for American option sensitivities estimation and a multilevel Monte Carlo simulation approach for portfolio risk estimation. / In the first part, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem when it has model uncertainty. We introduce a generalized IPA approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter. The unbiased price-sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high dimensional environments and various process settings. We can easily embed them into many of the most popular pricing algorithms without extra simulation effort to obtain sensitivities as a by-product of the option price. This generalized approach also casts new insights on how to perform sensitivity analysis using IPA: we do not need pathwise differentiability to apply it. Another contribution of this chapter is to investigate how the estimation quality of sensitivities will be affected by the quality of approximated exercise times. / In the second part, we propose a multilevel nested simulation approach to estimate the expectation of a nonlinear function of a conditional expectation, which has a direct application in portfolio risk estimation problems under various risk measures. Our estimator consists of a linear combination of several standard nested estimators. It is very simple to implement and universally applicable across various problem settings. The results of theoretical analysis show that the algorithmic complexities of our estimators are independent of the problem dimensionality and are better than other alternatives in the literature. Numerical experiments, in both low and high dimensional settings, verify our theoretical analysis. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liu, Yanchu. / "December 2012." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 89-96). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.iii / Acknowledgements --- p.v / Contents --- p.vii / List of Tables --- p.ix / List of Figures --- p.xii / Chapter 1. --- Overview --- p.1 / Chapter 2. --- American Option Sensitivities Estimation via a Generalized IPA Approach --- p.4 / Chapter 2.1. --- Introduction --- p.4 / Chapter 2.2. --- Formulation of the American Option Pricing Problem --- p.10 / Chapter 2.3. --- Main Results --- p.14 / Chapter 2.3.1. --- A Generalized IPA Approach in the Presence of a Decision Variable --- p.16 / Chapter 2.3.2. --- Unbiased First-Order Sensitivity Estimators --- p.21 / Chapter 2.4. --- Implementation Issues and Error Analysis --- p.23 / Chapter 2.5. --- Numerical Results --- p.26 / Chapter 2.5.1. --- Effects of Dimensionality --- p.27 / Chapter 2.5.2. --- Performance under Various Underlying Processes --- p.29 / Chapter 2.5.3. --- Effects of Exercising Policies --- p.31 / Chapter 2.6. --- Conclusion Remarks and Future Work --- p.33 / Chapter 2.7. --- Appendix --- p.35 / Chapter 2.7.1. --- Proofs of the Main Results --- p.35 / Chapter 2.7.2. --- Likelihood Ratio Estimators --- p.43 / Chapter 2.7.3. --- Derivation of Example 2.3 --- p.49 / Chapter 3. --- Multilevel Monte Carlo Nested Simulation for Risk Estimation --- p.52 / Chapter 3.1. --- Introduction --- p.52 / Chapter 3.1.1. --- Examples --- p.53 / Risk Measurement of Financial Portfolios --- p.53 / Derivatives Pricing --- p.55 / Partial Expected Value of Perfect Information --- p.56 / Chapter 3.1.2. --- A Standard Nested Estimator --- p.57 / Chapter 3.1.3. --- Literature Review --- p.59 / Chapter 3.1.4. --- Summary of Our Contributions --- p.61 / Chapter 3.2. --- The Multilevel Approach --- p.63 / Chapter 3.2.1. --- Motivation --- p.63 / Chapter 3.2.2. --- Multilevel Construction --- p.65 / Chapter 3.2.3. --- Theoretical Analysis --- p.67 / Chapter 3.2.4. --- Further Improvement by Extrapolation --- p.69 / Chapter 3.3. --- Numerical Experiments --- p.72 / Chapter 3.3.1. --- Single Asset Setting --- p.73 / Chapter 3.3.2. --- Multiple Asset Setting --- p.74 / Chapter 3.4. --- Concluding Remarks --- p.77 / Chapter 3.5. --- Appendix: Technical Assumptions and Proofs of the Main Results --- p.79 / Bibliography --- p.89

Cardiovascular disease remains one of the leading causes of mortality globally. Innovative techniques are required to tackle its anticipated rise due to rising obesity, diabetes and an ageing population. Personalised electronic coaching (eb coaching) using the Internet and emails may help motivate healthier living and be of clinical benefit in complementing current programmes for cardiovascular risk reduction. I investigated whether personalised ebcoaching on top of SOC was more clinically effective than SOC alone, in reducing cardiovascular risk in asymptomatic individuals with high cardiovascular risk. I lead a randomised controlled trial of 402 participants using robust surrogate markers to identify change over 6 months. I assessed the feasibility of using cardiovascular magnetic resonance surrogate markers to guide their use in future studies of lifestyle interventions. I performed systematic reviews to identify 1) similarities and differences among leading primary prevention guidelines that address cardiovascular screening and risk assessment and 2) guideline recommendations on lifestyle advice and interventions to identify how ebcoaching could be used and what advice to incorporate in ebcoaching platforms. I found modest but statistically significant improvements in both ebcoaching and SOC groups to a similar level. Personalised ebcoaching did not show additional benefit in a highbrisk primary prevention cohort. It is feasible to use cardiovascular surrogate markers derived from cardiovascular magnetic resonance in lifestyle interventions studies. However, further studies correlating change in these markers with longbterm outcomes are required. Considerable discrepancies exist in the guidelines on risk on cardiovascular screening and risk assessment, with no consensus on optimum screening strategies or classification of high risk thus affecting treatment threshold. Guidelines did highlight the importance of lifestyle interventions in primary prevention and generally provided similar advice. Ebcoaching should not be incorporated into current prevention programmes for high risk populations unless the tools are improved and effectiveness is proven.

Criminogenic risk assessment, which was developed to predict recidivism, has risen to the status of “evidence-based practice” in corrections systems. As a result of its apparent success, proponents now claim that it captures the origins of criminal behavior, and can thus be leveraged to reduce correctional supervision rates and prevent crime. This dissertation investigates the validity of the these claims, by identifying and testing three assumptions requisite for the framework’s expansion: 1) the evidence base for the framework’s predictive performance is being interpreted correctly and appropriately, 2) the best causal models of recidivism are also the best causal models of the onset and duration of criminal behavior (and by extension, that interventions successful at reducing recidivism will be successful at reducing the onset, duration, and rate of criminal behavior); and 3) the causes of individual variation in criminal behavior are the same as causes of the population distribution, or incidence rate, of crime. This dissertation proceeds in three parts: a meta-review and critical analysis of the literature addresses the first assumption, and two empirical studies test the second and third assumptions, respectively. The meta-review determined that findings for the framework’s predictive performance are inconsistent, based on inadequate or insufficient statistical information, and often overstated. The first empirical study found that each arrest, and to a lesser extent conviction, an individual experienced increased their subsequent criminogenic risk levels, raising concerns about the framework’s applicability for crime prevention and etiology. The second empirical study found that criminogenic risks do not explain group differences in arrest and conviction rates, underscoring that researchers and policymakers should more cautiously communicate the scope of reform that the framework can deliver.

博士論文著重研究關於多項式優化的理論，並討論其在風險管理及統計分析中的應用。我們主要研究的對象乃為在控制理論和穩健優化中常見的所謂S 引理。原始的S 引理最早由Yakubovich 所引入。它給出一個二吹多項式在另一個二吹多項式的非負域上為非負的等價條件。在本論文中，我們把S 引理推廣到一元高吹多項式。由於S 引理與穩健優化密切相關，所以我們的結果可廣泛應用於風險管理及統計分析，包括估算在高階矩約束下的非線性風險量度問題，以及利用半正定規劃來計算同時置信區域帶等重要課題。同時，在相關章節的末段，我們以數值實驗結果來引證有關的新理論的有效性和應用前景。 / In this thesis we study some structural results in polynomial optimization, with an emphasis paid to the applications from risk management problems and estimations in statistical analysis. The key underlying method being studied is related to the so-called S-lemma in control theory and robust optimization. The original S-lemma was developed by Yakubovich, which states an equivalent condition for a quadratic polynomial to be non-negative over the non-negative domain of other quadratic polynomial(s). In this thesis, we extend the S-Lemma to univariate polynomials of any degree. Since robust optimization has a strong connection to the S-Lemma, our results lead to many applications in risk management and statistical analysis, including estimating certain nonlinear risk measures under moment bound constraints, and an SDP formulation for simultaneous confidence bands. Numerical experiments are conducted and presented to illustrate the effectiveness of the methods. / Detailed summary in vernacular field only. / Wong, Man Hong. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 134-147). / Abstract also in Chinese. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Meeting the S-Lemma --- p.5 / Chapter 3 --- A strongly robust formulation --- p.13 / Chapter 3.1 --- A more practical extension for robust optimization --- p.13 / Chapter 3.1.1 --- Motivation from modeling aspect --- p.13 / Chapter 3.1.2 --- Discussion of a more robust condition --- p.15 / Chapter 4 --- Theoretical developments --- p.19 / Chapter 4.1 --- Definition of several order relations --- p.19 / Chapter 4.2 --- S-Lemma with a single condition g(x)≥0 --- p.20 / Chapter 5 --- Confidence bands in polynomial regression --- p.47 / Chapter 5.1 --- An introduction --- p.47 / Chapter 5.1.1 --- A review on robust optimization, nonnegative polynomials and SDP --- p.49 / Chapter 5.1.2 --- A review on the confidence bands --- p.50 / Chapter 5.1.3 --- Our contribution --- p.51 / Chapter 5.2 --- Some preliminaries on optimization --- p.52 / Chapter 5.2.1 --- Robust optimization --- p.52 / Chapter 5.2.2 --- Semidefinite programming and LMIs --- p.53 / Chapter 5.2.3 --- Nonnegative polynomials with SDP --- p.55 / Chapter 5.3 --- Some preliminaries on linear regression and confidence region --- p.59 / Chapter 5.4 --- Optimization approach to the confidence bands construction --- p.63 / Chapter 5.5 --- Numerical experiments --- p.66 / Chapter 5.5.1 --- Linear regression example --- p.66 / Chapter 5.5.2 --- Polynomial regression example --- p.67 / Chapter 5.6 --- Conclusion --- p.70 / Chapter 6 --- Moment bound of nonlinear risk measures --- p.72 / Chapter 6.1 --- Introduction --- p.72 / Chapter 6.1.1 --- Motivation --- p.72 / Chapter 6.1.2 --- Robustness and moment bounds --- p.74 / Chapter 6.1.3 --- Literature review in general --- p.76 / Chapter 6.1.4 --- More literature review in actuarial science --- p.78 / Chapter 6.1.5 --- Our contribution --- p.79 / Chapter 6.2 --- Methodological fundamentals behind the moment bounds --- p.81 / Chapter 6.2.1 --- Dual formulations, duality and tight bounds --- p.82 / Chapter 6.2.2 --- SDP and LMIs for some dual problems --- p.84 / Chapter 6.3 --- Worst expectation and worst risk measures on annuity payments --- p.87 / Chapter 6.3.1 --- The worst mortgage payments --- p.88 / Chapter 6.3.2 --- The worst probability of repayment failure --- p.89 / Chapter 6.3.3 --- The worst expected downside risk of exceeding the threshold --- p.90 / Chapter 6.4 --- Numerical examples for risk management --- p.94 / Chapter 6.4.1 --- A mortgage example --- p.94 / Chapter 6.4.2 --- An annuity example --- p.97 / Chapter 6.5 --- Conclusion --- p.100 / Chapter 7 --- Computing distributional robust probability functions --- p.101 / Chapter 7.1 --- Distributional robust function with a single random variable --- p.105 / Chapter 7.2 --- Moment bound of joint probability --- p.108 / Chapter 7.2.1 --- Constraint (7.5) in LMIs --- p.112 / Chapter 7.2.2 --- Constraint (7.6) in LMIs --- p.112 / Chapter 7.2.3 --- Constraint (7.7) in LMIs --- p.116 / Chapter 7.3 --- Several model extensions --- p.119 / Chapter 7.3.1 --- Moment bound of probability of union events --- p.119 / Chapter 7.3.2 --- The variety of domain of x --- p.120 / Chapter 7.3.3 --- Higher moments incorporated --- p.123 / Chapter 7.4 --- Applications of the moment bound --- p.124 / Chapter 7.4.1 --- The Riemann integrable set approximation --- p.124 / Chapter 7.4.2 --- Worst-case simultaneous VaR --- p.124 / Chapter 7.5 --- Conclusion --- p.126 / Chapter 8 --- Concluding Remarks and Future Directions --- p.127 / Chapter A --- Nonnegative univariate polynomials --- p.129 / Chapter B --- First and second moment of (7.2) --- p.131 / Bibliography --- p.134

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