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Event(s) on May 2006
- 2/5/2006
| 題目: |
Ruin Probability in Personal Finance |
| 講員: |
Prof. Huaxiong Huang, Department of Mathematics and Statistics, York University, Canada |
| 時間/地點: |
11:30 - 12:30
FSC 1217
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| 摘要: |
In this talk we discuss ruin probability in retirement planning.
Using a PDE based approach, we show how the runied probability
can be computed efficiently using numerical methods. In the second
half of the talk, we will focus on the effect of stochastic inflation
rate on the retirement planning as more and more companies started
to offer inflation-linked funds. In particular, we discuss the
optimal asset allocation strategy between a CPI-linked bond fund
and an equity-based fund for a retiree facing a stochastic consumption
liability stream. We focus financial attention on the demand
for CPI-linked bonds as a hedge against retiree's personal inflation
rate. Our results confirm some of the strategies in practice
but also reveal some highly non-intuitive strategies.
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- 23/5/2006
| 題目: |
On Dispersal and Population Growth for Multistate Matrix Models |
| 講員: |
Prof. Chi-Kwong Li, Department of Mathematics, The College of William and Mary, USA |
| 時間/地點: |
11:30 - 12:30
FSC 1217
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| 摘要: |
To describe the dynamics of stage-structured populations with
m stages
living in n patches, we consider matrix models of the form S,
D where
S is a block diagonal matrix with n-by-n column substochastic
matrices S_1,...,S_m along the diagonal and D is a block matrix
whose blocks are n-by-n nonnegative diagonal matrices. The matrix
S
describes movement between patches and the matrix D describes
growth and
reproduction within the patches. Consider the multiple arc directed
graph
G consisting of the directed graphs corresponding to the matrices
S_1,...,S_m where each directed graph is drawn in a different
color.
We say G has a polychromatic cycle if G has a directed cycle
that
includes arcs of more than one color. We prove that the spectral
radius of
SD is not larger than that of D for all block matrices D with
nonnegative diagonal blocks if and only if G has no polychromatic
cycle.
Applications to ecological models are presented.
[This is joint work with Sebastian J. Schreiber (William and
Mary).
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- 26/5/2006
| 題目: |
SRCC - Dimension Reduction: Data Analysis and Current Fronties |
| 講員: |
Prof. Bing Li, Department of Statistics, The Pennsylvania State University, USA |
| 時間/地點: |
11:30 - 12:30
FSC 1217
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| 摘要: |
The recent computing revolution has produced an unprecedented
capacity for data processing and storage, motivated and followed
by advances in a number of research fields. Dimension reduction
is a powerful means to eliminate redundancy and identify informational
cores in complex and often overwhelmingly large data sets.
As such its research has gained tremendous momentum since its
introduction in the early 90s. In this talk I will give a general
introduction and overview of the current research in dimension
reduction: its motivations, its basic principles, its important
results, and its main areas of applications. As much as possible
I will illustrate the key issues by data analysis.
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