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.

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.

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.

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.

2007年美國爆發次級房貸違約潮造成了其經濟、房市和股市的不景氣，也波及到持有美國房貸證券化商品的各國，使其承受重大的損失，因此房屋抵押貸款違約的影響因素和金融資產證券化機制對貸款違約風險的影響又再度成為不動產與金融市場上之重要議題。而以往針對美國次貸危機的研究多指出道德風險是造成此次危機的原因之一，但是較缺乏實證研究的支持。 有鑑於此，本研究以我國的台北市和新北市的房屋抵押貸款市場作為研究對象，探討逆選擇和道德風險這兩個資訊不對稱的問題對貸款違約率的影響。研究結果顯示「貸款成數高、貸款利率高、搭配信貸和設定二胎的貸款比較容易違約」，證實逆選擇和道德風險問題確實存在於房屋抵押貸款市場，而且會增加貸款違約的機率。為了降低違約機率，從降低資訊不對稱的角度來看，本研究建議：一、建立全國房貸資料庫；二、將信貸的金額納入房貸的貸款成數中考慮，以降低款人的道德風險。 再者，本研究認為造成次貸危機的根本原因是不當政策導致的保證機制浮濫，以及高風險的房貸證券化商品的氾濫。為了避免我國發生類似次貸危機的事件，從減少資訊不對稱的角度切入，本研究建議我國的金融資產證券化機制應該：一、將道德風險內部化，消除創始機構自利的動機以減少道德風險；二、使用外部信用增強的方式，以確實發揮分散證券風險的作用。 / The 2007 subprime mortgage crisis has severely struck the stability of the worldwide financial markets. Some researches indicate that moral hazard problems are the main factors causing the crisis. However, few studies support asymmetry problems existing in a mortgage market by empirical evidences. First, using the mortgage samples from Taipei City and New Taipei City this study would like to understand if the mortgage market are information asymmetry problems, adverse selection and moral hazard, and conduct the empirical analysis for these factors’ impact on mortgage default. The results show that mortgage default is influenced significantly by the Loan-to-Value （LTV） ratio, contract interest rates, the existence of second liens and credit loans, and jobs. It shows that adverse selection and moral hazard actually exist in the mortgage market. According to the empirical results, secondly, this study proposes suggestions for mortgage lending and financial asset securitization to reduce adverse selection and moral hazard problems and enhance the regulation environment and market’s stability. It is expected that the results of this study will be applied to avoid the occurrence of similar crisis in Taiwan.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 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 mortgage origination, data as well as bank bailouts. 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 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 sequel, 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). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). 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, bailout or policymaking role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - 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 SORs' capital, information, ratings, risk and 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 loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 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 mortgage origination, data as well as bank bailouts. 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 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 sequel, 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). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). 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, bailout or policymaking role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - 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 SORs' capital, information, ratings, risk and 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 loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]). / Thesis (Ph.D. (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.

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.