Annual Report 2008.pdf - SAMSI

suggested modeling the loss as a beta distributed random variable times a constant and then look
at the expected loss. For the second course, I focused on modeling financial time series. I worked
together with Dr. Munoz on modeling five stocks from the European market. For these series, we
found that the models that fit best are GARCH or E-GARCH with t distributed errors.
My contribution to the working groups consisted in participating in discussions and
holding two presentations. In the Multivariate Extremes Applications working group I presented
the earlier mentioned financial time series project. I also participated in the Multivariate
extremes Methodology working group where I presented a paper for analyzing time series data
following the Poisson distribution. This paper was proposed by Dr. Smith as a method to be used
to analyze hurricane occurrences in the Atlantic and investigate the correlation with sea surface
temperature; his idea was to analyze the two variables as a bivariate time series to remove the
autocorrelation and then test for correlation between them.
During the SAMSI undergraduate workshops, I had the opportunity to provide students
with an introduction to the methodology for extreme value analysis. At the same time, I guided
students in the use of computer software in the practice session. During breaks I had the
opportunity to talk to them and answer their questions regarding graduate studies. Among other
activities, I also attended the SAMSI seminars, where I became familiar with typical extreme
value analysis topics such as modeling the dependence on extreme values for different variables
and estimation of the parameters of M4 processes. Overall, these seminars have nurturedand
greatly expanded my interest and knowledge in extreme value theory, both at a theoretical
andpractical level.
2. Random Media
Qin Zhang (NCSU) has been active in two working groups at SAMSI. One is the working group
on Interface Problems. He took the SAMSI course MA581 in the fall 2007 on free boundaries
and moving interfaces. He is also one of participants of the SAMSI working group on stochastic
PDE. He gave a presentation, titled “Optimal Bilinear Control on Quantum Systems,” in the
SAMSI Postdoc/Graduate Students Seminar. He also presented a talk on the quantum
probability theory and quantum filtering problems in the working group. His thesis topic
concerns finding a stable feedback solution for quantum control problem arisen in quantum spin
systems under continuous measurement which is closed related to the SAMSI program. He also
helped with the undergraduate workshop.
Ke Xu (UNC) was involved in the heterogeneity in biological media working group. She took
the SAMSI course MA581 in the fall 2007 on free boundaries and moving interfaces. She spoke
in the working group several time about her research and relation with the SAMSI program.
Hui Xie (NCSU) is involved in the interface working group. Hui Xie is a graduate student at
NCSU working toward his Ph.D. He took the SAMSI course MA581 in the fall, 2007 on
numerical methods for free boundaries and moving interfaces. He presented a talk in the
interface working group. His talk was about the finite element method with a locally modified
triangulation for the elliptic interface problems. He also helped with the undergraduate
workshop.