GIT for student Yuxiang Huang. The student is expected to build predictive models for mortgage credit risk and default probabilities, using mathematical and statistical methods, such as Markov Chain, linear regression, logistic regression, and machine learning technologies. The student is also expected to perform all aspects of model design and development such as data gathering, data analysis, reconciliation, modeling, research, and testing.

The student, Yang Zhao, will provide research and services on projects related to financial risk management and econometric models.

The PI will supervise the student to work with Genworth on preparation on a multi-year forecast for the development of insured loans portfolio and will conduct model testing and evaluating the results. Jeffrey Scroggs will be the University������������������s Project Coordinator/Faculty Advisor and Ed Hartman will be the Sponsor������������������s on-site supervisor during the term of this agreement. These individuals will monitor the performance of the Student through periodic informal contact.

Duties: NCSU through the GIT Student will provide research and analysis to SAS as set forth in this Agreement. Such research and analysis shall include, but is not limited to, research, generation, testing, and documentation of operations research software. GIT Student will provide such services for SAS offices in Cary, North Carolina, at such times as have been mutually agreed upon by the parties. GIT Student agrees to abide by SAS policies and procedures regarding security of SAS facilities and computing resources. GIT Student further agrees to submit to background verification. If SAS, in its sole discretion, find GIT Student's background unsuitable, this Agreement shall terminate immediately.

The PI will supervise the student to work with Genworth on problems in mortgage backed securities and financial risk management. In particular, the student will work on the prepayment model developing and default probability estimations.

Topics in Stochastic Control Theory and Its Applications A very common but very important issue in our practical life is how to minimize the associated costs or maximize the payoffs of certain operations or procedures. Due to the unpredictability of our real world, this kind of problems can be modeled by stochastic control problems. We propose a research project on PDE method and numerical method in stochastic control theory and applications. In most cases, the solution of stochastic control problem depends on how to solve the associated Hamilton-Jacobi-Bellman (HJB) equation. HJB equations are usually second order nonlinear partial differential equations and the existence result of the solutions is not always available. We have an efficient sub/super solution method to determine whether the solution exists or not for certain types of HJB equations. We plan to extend the current results to more general cases, especially to the high dimensional cases. Viscosity solution method is very useful when there are some discontinuities due to jumps from unexpected events. In these cases, the HJB equation may not possess a classical solution. The viscosity solution is now widely used for non-smooth analysis, but the current results are not enough for stochastic control theory. We proposed a research to extend the current results to our proposed stochastic control problems. The proposed project also includes the research on numerical method. The HJB equation has explicit solutions only in very simple cases. Although the existence results can be obtained using the sub/super solution method or viscosity solution method, in most cases numerical methods are needed to get the numerical solutions. We are going to study numerical methods for certain type of stochastic optimization problems. The key idea is to use Markov chain approximation and many technical difficulties need to be overcome.