本研究同時探討房貸違約與提前清償終止行為，並對提前清償動機『出售』與『轉貸』予兼容並蓄。蒐集自H銀行房貸資料，運用多項式邏吉斯廻歸模型分析法，以總體經濟因子之有無分兩階段，對應變數-房貸終止行為(Y1)及提前清償動機(Y2)，採取雙層次深入實證。 實證結果：從機率模型配適度與解釋力之實證分析中，獲得一致結論，對於含有總體經濟因子-經濟成長率與CPI 年增率之模型，其所計算Cox & Snell及Nagelkerke之假 值分別為0.534及0.611，均大於0.5以上，其相對性與獨立性上，均具備較高的模型解釋力，為一較優之房貸違約與提前清償終止行為模型，其相關顯著影響因子如下： 一、對違約具有顯著影響之因子，包括：借款年限、初貸利率、LTV、保證人、次級房貸、部分提前清償、購屋投資、 PTI、DBR＞22、軍警公教人員、設二胎、區域台北市、區域新北市及CPI年增率等14項。 二、對提前清償具有顯著影響之因子，包括：初貸利率、次級房貸、部分提前清償、購屋投資、購屋自住、年資、設二胎、CPI年增率及經濟成長率等9項。 三、對提前清償動機-『出售』之顯著因子：次級房貸、部分提前清償、購屋投資、設二胎等4項。 四、對提前清償動機-『轉貸』之顯著因子：初貸利率、次級房貸、購屋自住、年資、設二胎、CPI年增率及經濟成長率等7項。。 本實證結果所建構含有總體經濟因子之房貸終止行為機率模型，以其顯著影響因子再深入探討提前清償-『出售』與『轉貸』之動機，使提前清償行為模式更精確性地呈現，有助於提供金融機構，在計算違約機率與提前清償機率之模型架構上及授信審核評估上，具貢獻價值之參考資訊。 / This research explores the default and prepayment on the termination behaviors of residential mortgages, as well as the motives of prepayment in house selling or refinancing. Mortgage data are collected from the H bank in Taiwan, using the multi-nominal logistic regression analytic method to explore the factors affecting the default and prepayment behaviors. Empirical results show that loan period, initial mortgage rate, loan-to-value ratio (LTV), the existence of the guarantor, subprime mortgages, curtailment, investment purpose, payment-to-income (PTI), debt burden ratio exceeded 22 (DBR＞22), government employees or teachers, second lien, location in Taipei city, the new Taipei city and CPI annual rate of increase are the significant factors of default behavior. As for the variables on prepayment, the initial mortgage rate, subprime mortgages, curtailment, investment purpose, residential use, DBR＞22, the age of professional career, second lien, CPI annual rate of increase and economical growth rate are significant. For more detailed curtailment behavior, the empirical results show that house sale subprime mortgages, curtailment, residential investment purpose, second lien are significant factors. As for the variables in inter-bank refinancing initial interest rate, subprime mortgages, residential investment purpose, the age of professional career, second lien, CPI annual rate of increase and economical growth rate are significant factors. Results of this research may provide financial institutions precious references on the mortgage default and prepayment behaviors. The mortgage industry can take into account of the significant results on the capital planning in the future.

Submitted by Dani Arruda (arrudadani@gmail.com) on 2017-03-31T18:01:38Z No. of bitstreams: 1 Dissertação Daniel Sivieri Arruda - Final 31.03.2017.pdf: 2886477 bytes, checksum: e7db064cbaa7bb943ecd1527d65cc458 (MD5) / Approved for entry into archive by Leiliane Silva (leiliane.silva@fgv.br) on 2017-03-31T19:20:28Z (GMT) No. of bitstreams: 1 Dissertação Daniel Sivieri Arruda - Final 31.03.2017.pdf: 2886477 bytes, checksum: e7db064cbaa7bb943ecd1527d65cc458 (MD5) / Made available in DSpace on 2017-04-12T19:00:31Z (GMT). No. of bitstreams: 1 Dissertação Daniel Sivieri Arruda - Final 31.03.2017.pdf: 2886477 bytes, checksum: e7db064cbaa7bb943ecd1527d65cc458 (MD5) Previous issue date: 2017-02-15 / Os eventos financeiros do período 2007-2009 - crise do subprime - mostraram algumas das fragilidades das instituições financeiras. Os mecanismos de resolução bancária – ferramentas de reestruturação de instituições financeiras realizada pela autoridade de resolução, para garantir a continuidade das funções em crise, preservação da estabilidade financeira e reestruturação da viabilidade financeira total ou em parte - até então existentes não foram capazes de resolver o problema das instituições 'too big to fail'. O governo americano, assim como de outros países, foi obrigado a realizar um grande programa de resgate com utilização de recursos públicos, o bailout. Na tentativa de evitar o uso de recursos públicos, o Financial Stability Board, implementou novos mecanismos de resolução bancária com vistas a incentivar soluções de mercado, o bail-in, em oposição ao bail-out. O presente trabalho aborda as discussões envolvendo a regulação do sistema financeiro, a incapacidade dos mecanismos de primeira geração em lidar com a crise do subprime, e os instrumentos criados pós crise. Assim, versa sobre os motivos que levam a necessidade de se regular bancos, os problemas das instituições 'too big to fail' e a necessidade de criar novos mecanismos de resolução bancária para instituições financeiras em dificuldades. Nesse sentido, aborda a estrutura e a aplicação das normas criadas pós crise financeira do subprime, em especial os Key Attributes of Effective Resolution Regimes of Financial Institutions, elaborado pelo FSB, que estabelecem os standards internacionais para resolução de instituições financeiras. O trabalho analisa a agenda de reforma internacional, em especial a que ocorre nos EUA e Europa. Para isso, aborda, também, os instrumentos criados pela BRRD, na Europa, e o Dodd-Frank Act, dos EUA, mostrando suas características e diferenças. Por fim, ao concluir, analisa que os instrumentos criados fazem parte de um grande consenso internacional sobre os planos de resolução e recuperação dos bancos, bem como o papel do regulador bancário em reação aos eventos financeiros recentes. A questão sobre se os planos irão contribuir significativamente para garantir a resolvabilidade de grandes instituições financeiras sistemicamente relevantes ainda é algo em aberto. A complexidade da inovação financeira e das instituições podem dificultar uma avaliação mais precisa sobre a efetividade dos planos de resolução.

Uma característica marcante da recente crise financeira que ocorreu entre 2007 e 2009, conhecida como \"A Crise do Subprime\", foi quão rapidamente se propagou por todo o mundo. Entretanto, a maior parte da evidência empírica até o presente momento mostra que no início da crise (jun/07 - ago/08) a resposta das economias emergentes foi limitada. Este trabalho corrobora este fato, bem como a rápida saída da crise, para um grupo de países emergentes em acelerado processo de desenvolvimento: Brasil, Rússia, Índia e China, os BRICs. Encontramos ainda evidências de que a China exerceu, principalmente durante a crise, forte impacto positivo nos BRICs, o que nos levou a concluir que este foi um fator importante para que fossem menos afetados, quando comparados com economias desenvolvidas como os EUA. Também mostramos que países dentre os BRICs cuja atividade econômica apresenta maior semelhança - Brasil X Rússia e Índia X China - são afetados de modo geral de forma análoga e observamos ainda evidência de notáveis ligações financeiras entre os países do grupo. Por último, notamos que variáveis reais dos BRICs responderam com menor intensidade aos efeitos da crise quando comparadas a variáveis financeiras do próprio grupo e variáveis reais de países desenvolvidos. Para o estudo, utilizamos modelos S-VAR, VEC e testes de cointegração em painel, este último para os modelos com variáveis macroeconômicas reais. Também utilizamos um índice de propagação de calor, desenvolvido pelo Fundo Monetário Internacional (FMI), que mede a intensidade dos efeitos da crise nas variáveis para cada instante do tempo. / One of the main characteristics of the recent financial crisis that took place between 2007 and 2009, known as \"The Subprime Crisis\", was how fast it spread all around the globe. Nevertheless, most empirical evidence shows that at the beginning of the crisis (Jun/07- Aug/08) emerging markets\' response was limited. This present study corroborates this idea for a fast raising group of emerging economies: Brazil, Russia, India and China, the BRICs. We show as well how rapid these economies have managed to get out of the crisis and the not negligent positive impact that China had in all of them, especially during the crisis period. We infer that China\'s booming economy must have been one of the main factors that made the crisis\' impact reduced for the BRICs when compared to developed countries such as the US. We also show that countries among the BRICs that have more similarities - Brazil X Russia and India X China - were in general affected in an analogous way and we observe that there are strong financial links between group members. Last, we find that the crisis\' effect on real BRIC\'s macroeconomic variables was not as intense as those on developed countries or on BRIC\'s financial variables. For this study, we use S-VAR, VEC and Panel Cointegration Models. This last one was used for models with real macroeconomic variables. To draw our conclusions, we also utilize a Heat Index which has been developed by the International Monetary Fund (IMF).This index is a measure of the crisis\' effects intensity on economic variables through time.

The main task of the diploma thesis is an analysis of financial performance and position of Morgan Stanley during several successive periods before and during the subprime financial crisis. Through the analysis of trends in key items, it also demonstrates strong cyclicality of financial performance and position of the investment bank. The first chapter deals with history and key divisions of the Company. The following chapter generally discusses selected phenomena, which, as per the author's view, significantly influenced industry-wide record-breaking performance during the period before the subprime crisis, and which substantially determined Morgan Stanley's risk profile and performance's corrections later during the Crisis. The core part of the Thesis is conceived as an analysis of financial performance and position of Morgan Stanley during the selected periods. The analysis of pre-crisis period until 2006 in the third chapter demonstrates growth of activities lying behind the unprecedented profitability of the Institution. The following fourth chapter analyzes deteriorating financial performance during the subprime crisis and indicates crucial strategy changes, implemented by the Company at the end of 2008. Effects of the strategic changes and challenges of the future development of the Institution are discussed in the last chapter. Additionally, the Thesis includes annexes, which further deal with selected topics and their general relations to investments banks and two annexes which compare Morgan Stanley with its nearest peers during specific periods.

This thesis aims to predict the probability of default (PD) of non-performing loan (NPL) customers using transaction and debt data, as a part of developing credit scoring model for Hoist Finance. Many NPL customers face financial exclusion due to default and therefore are considered as bad customers. Hoist Finance is a company that manages NPLs and believes that not all conventionally considered subprime customers are high-risk customers and wants to offer them financial inclusion through favourable loans. In this thesis logistic regression was used to model the PD of NPL customers at Hoist Finance based on 12 months of data. Different feature selection (FS) methods were explored, and the best model utilized l1-regularization for FS and predicted with 85.71% accuracy that 6,277 out of 27,059 customers had a PD between 0% to 10%, which support this belief. Through analysis of the PD it was shown that the PD increased almost linearly with respect to an increase in either debt quantity, original total claim amount or number of missed payments. The analysis also showed that the payment behaviour in the last quarter had the most predictive power. At the same time, from analysing the type II error it was shown that the model was unable to capture some bad payment behaviour, due to putting to large emphasis on the last quarter. / Det här examensarbetet syftar till att predicera sannolikheten för fallissemang för nödlidande lånekunder genom transaktions- och lånedata. Detta som en del av kreditvärdighetsmodellering för Hoist Finance. På engelska kallas sannolikheten för fallissemang för "probability of default" (PD) och nödlidande lån kallas för "non-performing loan" (NPL). Många NPL-kunder står inför ekonomisk uteslutning på grund av att de konventionellt betraktas som kunder med dålig kreditvärdighet. Hoist Finance är ett företag som förvaltar nödlidande lån och påstår att inte alla konventionellt betraktade "dåliga" kunder är högrisk kunder. Därför vill Hoist Finance inkludera dessa kunder ekonomisk genom att erbjuda gynnsamma lån. I detta examensarbetet har Logistisk regression används för att predicera PD på nödlidande lånekunder på Hoist Finance baserat på 12 månaders data. Olika metoder för urval av attribut undersöktes och den bästa modellen utnyttjade lasso för urval. Denna modell predicerade med 85,71 % noggrannhet att 6 277 av 27 059 kunder har en PD mellan 0 % till 10 %, vilket stödjer påståendet. Från analys av PD visade det sig att PD ökade nästan linjärt med avseende på ökning i antingen kvantitet av lån, det ursprungliga totala lånebeloppet eller antalet missade betalningar. Analysen visade också att betalningsbeteendet under det sista kvartalet hade störst prediktivt värde. Genom analys av typ II-felet, visades det sig samtidigt att modellen hade svårigheter att fånga vissa dåliga betalningsbeteende just på grund av att för stor vikt lades på det sista kvartalet.

La recrudescence des crises bancaires et financières place la problématique de la sécurité financière au centre des grands enjeux des politiques de régulation économique. En effet, la crise dite des Subprimes et les crises budgétaires y consécutives, puis la crise chypriote avec le sentiment de défiance du public qui en a résulté, amènent à penser que seule la sécurité financière permet de sauvegarder l’industrie financière malgré elle. Cet enjeu, plus pragmatique du reste, semble davantage trouver un écho en droit, contrairement à celui de stabilité financière qui apparait plutôt subjective, voire incantatoire.En Afrique centrale, comme dans les systèmes juridiques de tradition romano-latine, la question de la sécurité financière procède d’abord du statut juridique des déposants bancaires, de leur place dans l’ordre légal de désintéressement des créanciers, en cas défaillance. Mais la question de la sécurité d’un système bancaire intéresse aussi les établissements de crédit eux-mêmes, non simplement en raison de la nature risquée de leurs activités de transformation, mais surtout en raison de l’existence d’un risque systémique exacerbé par l’ingénierie financière. La question de la sécurité se pose dès lors non simplement en terme de protection des acteurs pris individuellement, mais davantage en terme de préservation voire de sauvegarde de l’outil économique qu’est le système bancaire et/ou financier. / The resurgence of banking and financial crises up the issue of financial security at the center of major policy issues of economic regulation. Indeed, the so-called subprime crisis and subsequent fiscal crises there, and the Cyprus crisis with a sense of public defiance that resulted, one may suggest that financial security will save the financial industry in spite of herself. This issue, more pragmatic moreover, seems to resonate more in law, unlike that of financial stability that appears rather subjective or incantatory. In Central Africa, as in the legal systems of Roman- Latin tradition, the question of financial security shall first the legal status of bank depositors, their place in the legal order of payment of creditors in the event of failure. But the question of the security of the banking system as interest credit institutions themselves, not simply because of the risky nature of their processing activities, but mainly because of the existence of systemic risk exacerbated by financial engineering. The question of safety arises therefore not simply in terms of protection of individual players , but more in terms of preservation or backup tool called economic banking and / or financial .

Subprime residential mortgage loan securitization and its associated risks have been a major topic of discussion since the onset of the subprime mortgage crisis (SMC) in 2007. In this regard, the thesis addresses the issues of subprime residential mortgage loan (RML) securitization in discrete-, continuous-and discontinuous-time and their connections with the SMC. In this regard, the main issues to be addressed are discussed in Chapters 2, 3 and 4. In Chapter 2, we investigate the risk allocation choices of an investing bank (IB) that has to decide between risky securitized subprime RMLs and riskless Treasuries. This issue is discussed in a discrete-time framework with IB being considered to be regret- and risk-averse before and during the SMC, respectively. We conclude that if IB takes regret into account it will be exposed to higher risk when the difference between the expected returns on securitized subprime RMLs and Treasuries is small. However, there is low risk exposure when this difference is high. Furthermore, we assess how regret can influence IB's view - as a swap protection buyer - of the rate of return on credit default swaps (CDSs), as measured by the premium based on default swap spreads. We find that before the SMC, regret increases IB's willingness to pay lower premiums for CDSs when its securitized RML portfolio is considered to be safe. On the other hand, both risk- and regret-averse IBs pay the same CDS premium when their securitized RML portfolio is considered to be risky. Chapter 3 solves a stochastic optimal credit default insurance problem in continuous-time that has the cash outflow rate for satisfying depositor obligations, the investment in securitized loans and credit default insurance as controls. As far as the latter is concerned, we compute the credit default swap premium and accrued premium by considering the credit rating of the securitized mortgage loans. In Chapter 4, we consider a problem of IB investment in subprime residential mortgage-backed securities (RMBSs) and Treasuries in discontinuous-time. In order to accomplish this, we develop a Levy process-based model of jump diffusion-type for IB's investment in subprime RMBSs and Treasuries. This model incorporates subprime RMBS losses which can be associated with credit risk. Furthermore, we use variance to measure such risk, and assume that the risk is bounded by a certain constraint. We are now able to set-up a mean-variance optimization problem for IB's investment which determines the optimal proportion of funds that needs to be invested in subprime RMBSs and Treasuries subject to credit risk measured by the variance of IE's investment. In the sequel, we also consider a mean swaps-at-risk (SaR) optimization problem for IB's investment which determines the optimal portfolio which consists of subprime RMBSs and Treasuries subject to the protection by CDSs required against the possible losses. In this regard, we define SaR as indicative to IB on how much protection from swap protection seller it must have in order to cover the losses that might occur from credit events. Moreover, SaR is expressed in terms of Value-at-Risk (VaR). Finally, Chapter 5 provides an analysis of discrete-, continuous- and discontinuous-time models for subprime RML securitization discussed in the aforementioned chapters and their connections with the SMC. The work presented in this thesis is based on 7 peer-reviewed international journal articles (see [25], [44], [45], [46], [47], [48] and [55]), 4 peer-reviewed chapters in books (see [42], [50j, [51J and [52]) and 2 peer-reviewed conference proceedings papers (see [11] and [12]). Moreover, the article [49] is currently being prepared for submission to an lSI accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2010.

The subprime mortgage crisis (SMC) is an ongoing housing and nancial crisis that was triggered by a marked increase in mortgage delinquencies and foreclosures in the U.S. It has had major adverse consequences for banks and nancial markets around the globe since it became apparent in 2007. In our research, we examine an originator's (OR's) nonlinear stochastic optimal control problem related to choices regarding deposit inflow rates and marketable securities allocation. Here, the primary aim is to minimize liquidity risk, more speci cally, funding and credit crunch risk. In this regard, we consider two reference processes, namely, the deposit reference process and the residential mortgage loan (RML) reference process. This enables us to specify optimal deposit inflows as well as optimal marketable securities allocation by using actuarial cost methods to establish an ideal level of subprime RML extension. In our research, relationships are established in order to construct a stochastic continuous-time banking model to determine a solution for this optimal control problem which is driven by geometric Brownian motion. In this regard, the main issues to be addressed in this dissertation are discussed in Chapters 2 and 3. In Chapter 2, we investigate uncertain banking behavior. In this regard, we consider continuous-time stochastic models for OR's assets, liabilities, capital, balance sheet as well as its reference processes and give a description of their dynamics for each stochastic model as well as the dynamics of OR's stylized balance sheet. In this chapter, we consider RML and deposit reference processes which will serve as leading indicators in order to establish a desirable level of subprime RMLs to be extended at the end of the risk horizon. Chapter 3 states the main results that pertain to the role of stochastic optimal control in OR's risk management in Theorem 2.5.1 and Corollary 2.5.2. Prior to the stochastic control problem, we discuss an OR's risk factors, the stochastic dynamics of marketable securities as well as the RML nancing spread method regarding an OR. Optimal portfolio choices are made regarding deposit and marketable securities inflow rates given by Theorem 3.4.1 in order to obtain the ideal RML extension level. We construct the stochastic continuoustime model to determine a solution for this optimal control problem to obtain the optimal marketable securities allocation and deposit inflow rate to ensure OR's stability and security. According to this, a spread method of RML financing is imposed with an existence condition given by Lemma 3.3.2. A numerical example is given in Section 3.5 to illustrates the main issues raised in our research. / Thesis (M.Sc. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

The subprime mortgage crisis (SMC) is an ongoing housing and nancial crisis that was triggered by a marked increase in mortgage delinquencies and foreclosures in the U.S. It has had major adverse consequences for banks and nancial markets around the globe since it became apparent in 2007. In our research, we examine an originator's (OR's) nonlinear stochastic optimal control problem related to choices regarding deposit inflow rates and marketable securities allocation. Here, the primary aim is to minimize liquidity risk, more speci cally, funding and credit crunch risk. In this regard, we consider two reference processes, namely, the deposit reference process and the residential mortgage loan (RML) reference process. This enables us to specify optimal deposit inflows as well as optimal marketable securities allocation by using actuarial cost methods to establish an ideal level of subprime RML extension. In our research, relationships are established in order to construct a stochastic continuous-time banking model to determine a solution for this optimal control problem which is driven by geometric Brownian motion. In this regard, the main issues to be addressed in this dissertation are discussed in Chapters 2 and 3. In Chapter 2, we investigate uncertain banking behavior. In this regard, we consider continuous-time stochastic models for OR's assets, liabilities, capital, balance sheet as well as its reference processes and give a description of their dynamics for each stochastic model as well as the dynamics of OR's stylized balance sheet. In this chapter, we consider RML and deposit reference processes which will serve as leading indicators in order to establish a desirable level of subprime RMLs to be extended at the end of the risk horizon. Chapter 3 states the main results that pertain to the role of stochastic optimal control in OR's risk management in Theorem 2.5.1 and Corollary 2.5.2. Prior to the stochastic control problem, we discuss an OR's risk factors, the stochastic dynamics of marketable securities as well as the RML nancing spread method regarding an OR. Optimal portfolio choices are made regarding deposit and marketable securities inflow rates given by Theorem 3.4.1 in order to obtain the ideal RML extension level. We construct the stochastic continuoustime model to determine a solution for this optimal control problem to obtain the optimal marketable securities allocation and deposit inflow rate to ensure OR's stability and security. According to this, a spread method of RML financing is imposed with an existence condition given by Lemma 3.3.2. A numerical example is given in Section 3.5 to illustrates the main issues raised in our research. / Thesis (M.Sc. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

Subprime residential mortgage loan securitization and its associated risks have been a major topic of discussion since the onset of the subprime mortgage crisis (SMC) in 2007. In this regard, the thesis addresses the issues of subprime residential mortgage loan (RML) securitization in discrete-, continuous-and discontinuous-time and their connections with the SMC. In this regard, the main issues to be addressed are discussed in Chapters 2, 3 and 4. In Chapter 2, we investigate the risk allocation choices of an investing bank (IB) that has to decide between risky securitized subprime RMLs and riskless Treasuries. This issue is discussed in a discrete-time framework with IB being considered to be regret- and risk-averse before and during the SMC, respectively. We conclude that if IB takes regret into account it will be exposed to higher risk when the difference between the expected returns on securitized subprime RMLs and Treasuries is small. However, there is low risk exposure when this difference is high. Furthermore, we assess how regret can influence IB's view - as a swap protection buyer - of the rate of return on credit default swaps (CDSs), as measured by the premium based on default swap spreads. We find that before the SMC, regret increases IB's willingness to pay lower premiums for CDSs when its securitized RML portfolio is considered to be safe. On the other hand, both risk- and regret-averse IBs pay the same CDS premium when their securitized RML portfolio is considered to be risky. Chapter 3 solves a stochastic optimal credit default insurance problem in continuous-time that has the cash outflow rate for satisfying depositor obligations, the investment in securitized loans and credit default insurance as controls. As far as the latter is concerned, we compute the credit default swap premium and accrued premium by considering the credit rating of the securitized mortgage loans. In Chapter 4, we consider a problem of IB investment in subprime residential mortgage-backed securities (RMBSs) and Treasuries in discontinuous-time. In order to accomplish this, we develop a Levy process-based model of jump diffusion-type for IB's investment in subprime RMBSs and Treasuries. This model incorporates subprime RMBS losses which can be associated with credit risk. Furthermore, we use variance to measure such risk, and assume that the risk is bounded by a certain constraint. We are now able to set-up a mean-variance optimization problem for IB's investment which determines the optimal proportion of funds that needs to be invested in subprime RMBSs and Treasuries subject to credit risk measured by the variance of IE's investment. In the sequel, we also consider a mean swaps-at-risk (SaR) optimization problem for IB's investment which determines the optimal portfolio which consists of subprime RMBSs and Treasuries subject to the protection by CDSs required against the possible losses. In this regard, we define SaR as indicative to IB on how much protection from swap protection seller it must have in order to cover the losses that might occur from credit events. Moreover, SaR is expressed in terms of Value-at-Risk (VaR). Finally, Chapter 5 provides an analysis of discrete-, continuous- and discontinuous-time models for subprime RML securitization discussed in the aforementioned chapters and their connections with the SMC. The work presented in this thesis is based on 7 peer-reviewed international journal articles (see [25], [44], [45], [46], [47], [48] and [55]), 4 peer-reviewed chapters in books (see [42], [50j, [51J and [52]) and 2 peer-reviewed conference proceedings papers (see [11] and [12]). Moreover, the article [49] is currently being prepared for submission to an lSI accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2010.