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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/4396 |
| Date | January 2010 |
| Creators | De Waal, Bernadine |
| Publisher | North-West University |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
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