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The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved heterogeneity of individual units and additive measurement errors. Another common way to model deterioration in civil engineering is to treat the rate of deterioration as a random variable. In the context of condition-based maintenance, the thesis shows that the random variable rate (RV) model is inadequate to incorporate temporal variability, because the deterioration along a specific sample path becomes deterministic. This distinction between the RV and GP models has profound implications to the optimization of maintenance strategies. The thesis presents detailed practical applications of the proposed models to feeder pipe systems and fuel channels in CANDU nuclear reactors. In summary, a careful consideration of the nature of uncertainties associated with deterioration is important for credible life-cycle management of engineering systems. If the deterioration process is affected by temporal uncertainty, it is important to model it as a stochastic process.

The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved heterogeneity of individual units and additive measurement errors. Another common way to model deterioration in civil engineering is to treat the rate of deterioration as a random variable. In the context of condition-based maintenance, the thesis shows that the random variable rate (RV) model is inadequate to incorporate temporal variability, because the deterioration along a specific sample path becomes deterministic. This distinction between the RV and GP models has profound implications to the optimization of maintenance strategies. The thesis presents detailed practical applications of the proposed models to feeder pipe systems and fuel channels in CANDU nuclear reactors. In summary, a careful consideration of the nature of uncertainties associated with deterioration is important for credible life-cycle management of engineering systems. If the deterioration process is affected by temporal uncertainty, it is important to model it as a stochastic process.

Nonparametric Bayesian inference has widespread applications in statistics and machine learning. In this thesis, we examine the most popular priors used in Bayesian non-parametric inference. The Dirichlet process and its extensions are priors on an infinite-dimensional space. Originally introduced by Ferguson (1983), its conjugacy property allows a tractable posterior inference which has lately given rise to a significant developments in applications related to machine learning. Another yet widespread prior used in nonparametric Bayesian inference is the Beta process and its extensions. It has originally been introduced by Hjort (1990) for applications in survival analysis. It is a prior on the space of cumulative hazard functions and it has recently been widely used as a prior on an infinite dimensional space for latent feature models. Our contribution in this thesis is to collect many diverse groups of nonparametric Bayesian tools and explore algorithms to sample from them. We also explore machinery behind the theory to apply and expose some distinguished features of these procedures. These tools can be used by practitioners in many applications.

Yes / Following the global financial crisis, the measurement of counterparty credit risk has become an essential part of the Basel III accord with credit value adjustment being one of the most prominent components of this concept. In this study, we extend the Merton structural credit risk model for counterparty credit risk calculation in the context of calculating the credit value adjustment mainly by estimating the probability of default. We improve the Merton model in a variance-convoluted-gamma environment to include default dependence between counterparties through a linear factor decomposition framework. This allows one to tackle dependence through a systematic common component. Our set-up allows for easier, faster and more accurate fitting for the credit spread. Results confirm that use of the variance-gamma-convolution clearly solves the vanishing credit spread problem for short time-to-maturity or low leverage cases compared to a Brownian motion environment and its modifications. / Ahmet Sensoy gratefully acknowledges support from Turkish Academy of Sciences under its Outstanding Young Scientist Award Programme (TUBA-GEBIP). Frank J. Fabozzi acknowledges the financial support from EDHEC Business School.

La thèse s’intéresse à l’étude du fonctionnement d’un système industriel. Il s’agit de proposer et de développer un nouveau modèle pour modéliser la dégradation accumulative d’un système. Le processus gamma standard est fréquemment utilisé pour étudier l’évolution de la détérioration d’un système. Toutefois, ce processus peut s’avérer inadapté pour décrire le phénomène de dégradation car le rapport variance sur moyenne est constant dans le temps, ce qui est relativement restrictif en pratique. Afin de surmonter cette restriction, nous proposons d’utiliser un processus gamma étendu introduit par Cinlar (1980), qui ne souffre plus de cette restriction. Mais ce dernier présente quelques difficultés techniques. A titre d’exemple, la loi d’un processus gamma étendu n’est pas connue sous une forme explicite. Ces difficultés techniques ont conduit Guida et al. (2012) à utiliser une version discrète d’un processus gamma étendu. Nous travaillons ici avec la version originale d’un processus gamma étendu en temps continu. Le but de ce mémoire est de développer des méthodes numériques permettant de quantifier les quantités fiabilistes associées et de développer des méthodes statistiques d’estimation des paramètres du modèle. Aussi, une autre partie de ce travail consiste à proposer une politique de maintenance dans le contexte d’un processus gamma étendu. / This thesis is dedicated to study the functioning of an industrial system. It is about proposing and developing a new model for modelling the accumulative degradation of a system. The standard gamma process is widely used to model the evolution of the system degradation. A notable restriction of a standard gamma process is that its variance-to-mean ratio is constant over time. This may be restrictive within an applicative context. To overcome this drawback, we propose to use an extended gamma process, which was introduced by Cinlar (1980). However, there is a cost and the use of an extended gamma process presents some technical difficulties. For example, there is no explicit formula for the probability distribution of an extended gamma process. These technical difficulties have lead Guida et al. (2012) to use a discrete version of an extended gamma process. We here propose to deal with the original continuous time version. The aim of this work is to develop numerical methods in order to compute the related reliability function and to develop statistical methods to estimate the parameters of the model. Also, another part of this work consists of proposing a maintenance policy within the context of an extended gamma process.

This thesis focuses on the parameter stability of additive normal tempered stable processes when calibrating a volatility surface. The studied processes arise as a generalization of Lévy normal tempered stable processes, and their main characteristic are their time-dependent parameters. The theoretical background of the subject is presented, where its construction is discussed taking as a starting point the definition of Lévy processes. The implementation of an option valuation model using Fourier techniques and the calibration process of the model are described. The thesis analyzes the parameter stability of the model when it calibrates the volatility surface of a market index (EURO STOXX 50) during three time spans. The time spans consist of the periods from Dec 2016 to Dec 2017 (after the Brexit and the US presidential elections), from Nov 2019 to Nov 2020 (during the pandemic caused by COVID-19) and a more recent time period, April 2023. The findings contribute to the understanding of the model itself and the behavior of the parameters under particular economic conditions.

本研究透過聯合系統與獨特風險綜合評估違約的強度，假設市場上經濟變數或資訊影響系統之違約強度，然若直接考慮所有經濟變數到模型中將可能會有共線性或維度過高之疑慮，因此透過狀態空間模型來設定狀態變數以及經濟變數之關係並將萃取三大狀態變數分別用以描述市場實質活動面、通貨膨脹以及信用環境。另外，將透過結構式模型來計算獨特性風險大小，當個別潛在的變數低於一定數值將導致個別的違約事件發生。而因布朗運動可能無法描述或校準市場上違約之鋒態以及偏態，將進一步考慮Variance Gamma過程用以更準確描述真實違約狀況。最後透過結合以上兩個風險綜合評估下，考慮一個聯合違約模型來評價信用違約交換之信用價差。 / Systematic and idiosyncratic risks are supposed to jointly trigger the default events. This paper identifies three fundamental risks to capture the systematic movement: real activity, inflation, and credit environment. Since most macroeconomic variables fluctuate together, the state-space model is imposed to extract the three variables from macroeconomic data series. In the idiosyncratic part, the structural model is applied. That is, idiosyncratic default is triggered by the crossing of a barrier. For improvement of the underlying lognormal distribution, we assume the process for the potential variable of the firm follows a Variance Gamma process, sufficient dimensions of which can fit the skewed and leptokurtic distributions. Under the specific setting of combinations of the two risks (the so-called joint default model), we price credit default swaps.

違約事件受到系統性風險與獨特性風險的綜合影響。本研究建構一狀態相依公司信用模型，該模型能反映出系統環境對市場造成的影響與個別公司獨特因子帶來的個別衝擊。 本模型透過從總體環境中萃取出的狀態變數來捕捉系統性變化，另外透過Variance Gamma過程來描繪個別公司的獨特因子帶來的影響。Variance Gamma過程可藉由調整分配的鋒態及偏態來調整布朗運動無法反映出的分配，以更貼近真實的市場訊息。 與縮減試模型相較之下，本模型無需參考信評機構的信用評等資訊，僅依賴市場上公開且透明的資訊，並且與結構式模型相同的是其富有經濟意涵。我們可以透過本模型來同時生成公司流動性危機發生機率與預期流動性危機造成的損失，進而利用本模型評價出個別公司信用違約交換的價格。 關鍵字：信用違約交換；系統風險；獨特性風險；狀態空間模型；Variance Gamma 過程 / Systematic and idiosyncratic risks are thought to affect the default events. This study develops a state-dependent corporate credit model that reflects both systematic movement and idiosyncratic shocks. To capture the systematic movement, the model extracts state factors from macroeconomics data. For the idiosyncratic part, the model applied Variance Gamma Process in depicting the potential variable of the firm by altering the distribution’s skewness and kurtosis. The model contains abundant economic significance as structural-form model does. Comparing to the reduced-form model, it does not rely on the information provided by rating agency but use information that is transparent and public. One can generate a firm’s probabilities of liquidity crisis and expected liquidity shortfalls endogenously and concurrently by employing the model. Credit derivative such as Single-name CDS can be priced under the model.

In this thesis, the structural model in credit risk and the credit derivatives is studied under both Black-Scholes setting and Variance Gamma (VG) setting. Using a Variance Gamma process, the distribution of the firm value process becomes asymmetric and leptokurtic. Also, the jump structure of VG processes allows random default times of the reference entities. Among structural models, the most emphasis is made on the Black-Cox model by building a relation between the survival probabilities of the Black-Cox model and the value of a binary down and out barrier option. The survival probabilities under VG setting are calculated via a Partial Integro Differential Equation (PIDE). Some applications of binary down and out barrier options, default probabilities and Credit Default Swap par spreads are also illustrated in this study.