Many analysts believe that problems in the U.S. housing market initiated the 2008–2010 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgages, securitization, as well as data. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination and securitization that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the thesis, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), SOR mortgage insurers (SOMIs), trustees, underwriters, credit rating agencies (CRAs), credit enhancement providers (CEPs) and monoline insurers (MLIs). Furthermore, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory or policymaking role. Most of the aforementioned agents and banks are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The main aspects of the SMC - subprime mortgages, securitization, as well as data - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of subprime SORs' risk and profit as well as their valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete–time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as mortgage losses. In addition, we show how high loan–to–value ratios due to declining housing prices curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 3 investigates the securitization of subprime mortgages into structured mortgage products such as subprime residential mortgage–backed securities (RMBSs) and collateralized debt obligations (CDOs). In this regard, our discussions focus on information, risk and valuation as well as the role of capital under RMBSs and RMBS CDOs. Our research supports the view that incentives to monitor mortgages has been all but removed when changing from a traditional mortgage model to a subprime mortgage model. In the latter context, we provide formulas for IB's profit and valuation under RMBSs and RMBS CDOs. This is illustrated via several examples. Chapter 3 also explores the relationship between mortgage securitization and capital under Basel regulation and the SMC. This involves studying bank credit and capital under the Basel II paradigm where risk–weights vary. Further issues dealt with are the quantity and pricing of RMBSs, RMBS CDOs as well as capital under Basel regulation. Furthermore, we investigate subprime RMBSs and their rates with slack and holding constraints. Also, we examine the effect of SMC–induced credit rating shocks in future periods on subprime RMBSs and RMBS payout rates. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 4 explores issues related to subprime data. In particular, we present mortgage and securitization level data and forge connections with the results presented in Chapters 2 and 3. The work presented in this thesis is based on 2 peer–reviewed chapters in books (see [99] and [104]), 2 peer–reviewed international journal articles (see [48] and [101]), and 2 peer–reviewed conference proceeding papers (see [102] and [103]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

This thesis describes the theory of model predictive control and application of the theory to synchronous drives. It shows explicit and on-line solutions and compares the results with classical vector control structure.

This thesis describes the theory of model predictive control and application of the theory to synchronous drives. It shows explicit and on-line solutions and compares the results with classical vector control structure.

Bien que la commande prédictive fasse appel à des paramètres ayant une signification concrète, la valeur de ces derniers impacte fortement les performances obtenues du système à contrôler. Leur réglage n’étant pas trivial, la littérature fait état d’un nombre conséquent de méthodes de réglage. Celles-ci ne garantissent cependant pas des valeurs optimales. L’objectif de cette thèse est de proposer une approche analytique et originale de réglage de ces paramètres. Initialement applicable aux systèmes MIMO linéaires, l’approche proposée a été étendue aux systèmes non linéaires avec ou sans contraintes et pour lesquels il existe un modèle Takagi-Sugeno (T-S). La classe des systemès non linéaires considérés ici est écrite sous la forme quasi-linéaire paramétrique (quasi-LPV). Sous l’hypothese que le système soit commandable et observable, la méthode proposée garantit la stabilité optimale de ce système en boucle fermée. Pour ce faire, elle s’appuie, d’une part, sur une technique d’amélioration du conditionnement de la matrice hessienne et, d’autre part, sur le concept de rang effectif. Elle présente également l’avantage de requérir une charge calculatoire moindre que celle des approches identifiées dans la littérature. L’intérêt de l’approche proposée est montré à travers l’application en simulation à différents systèmes de complexité croissante. Les travaux menés ont permis d’aboutir à une stratégie de commande prédictive auto-adaptative dénommée "ATSMPC" (Adaptive Takagi-Sugeno Model-based Predictive Control). / Even though predictive control uses concrete parameters, the value of these latter has a strong impact on the obtained performances from the system to be controlled. Their tuning is not trivial. That is why the literature reports a number of adjustment methods. However, these ones do not always guarantee optimal values. The goal of this thesis is to propose an analytical and original tuning tuning approach of these parameters. Initially applicable to linear MIMO systems, the proposed approach has been extended to non-linear systems with or without constraints and for which a Takagi-Sugeno (T-S) model exists. The class of nonlinear systems considered here is written in quasi-linear parametric form (quasi-LPV). Assuming that the system is controllable and observable, the proposed method guarantees the optimal stability of this closed-loop system. To do this, it relies, on the one hand, on a conditioning improving technique of the Hessian matrix and, on the other hand, on the concept of effective rank. It also has the advantage of requiring a lower computational load than the approaches identified in the literature. The interest of the proposed approach is shown through the simulation on different systems of increasingcomplexity. The work carried out has led to a self-adaptive predictive control strategy called "ATSMPC" (Adaptive Takagi-Sugeno Model-based Predictive Control).