- Monetary Systems
This STS project intends to give an overview of the monetary systems
adopted by our governments. The topics that may be tackled are:
- origins and evolution of currencies;
- emission of currency by the governments;
- the mains rules of a monetary policy;
- the exchange and interest rates (how are they set?);
- the mathematical models for exchange and interest rates.
The different topics may be treated separately by different students.
Requirements: motivation
For further information, please contact
Christophe D. Osinski.
Added on Friday, 01 March 2002
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- Metropolis-Hastings Algorithms for
Penalised Profile Likelihood
In the framework of penalised likelihood based inference, the
interpretation of the penalty as a prior density provides a good
justification for the use of bayesian techniques. However improper priors
are still questionable and lots of statiticians reject them. This project
aims to adapt Metropolis-Hastings algorithms in the case of the presence of
a nuisance parametre avoiding improper prior. This project will certainely
require fairely good skills in S-Plus coding, but, as it is a wide subject,
previous statiscal requirements can be adapted. However it should be more
interesting for someone who has already attended the Monte-Carlo Inference
course (or equivalent).
Requirements: motivation
For further information, please contact
Marc-Olivier Boldi.
Added on Friday, 19 October 2001
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- Volatility Structure of Stock Prices
In recent years many discrete time models have been developed to fit
financial data. Among the most popular are the ARCH family. One of
the last arrived in this family is the HARCH process. This process has many
nice proprieties like considering different levels in the volatility
depending on the time horizon of the investors.
The project would consist in learning about ARCH type processes, especially
HARCH and fitting those models to stock returns. Two interesting questions
then appear, the first one for ARCH type processes in general and the
second for the HARCH process:
- what is the quality of the fit?
- which kind of investor (short, middle, long-term) operates on the NASDAQ,
SMI, S&P500,...?
Requirements: knowledge in time series
For further information, please contact
Christophe D. Osinski.
Keywords: log-returns; volatility; t-distribution;
auto-correlation; cross-correlation; ARCH models
Added on Thursday, 11 January 2001
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- Image Denoising using Wavelets
Generalized Basis Pursuit, a recent denoising technique to denoise
image, involves solving an optimization problem. The technique is currently
using an interior point algorithm. The technique has already been
programed in Matlab but is slow for large images. The project would
consist in programing the same technique in a faster language like C or C++.
Requirements: good programming skills, some mathematics, interest in
image processing, motivation
If you want further information, please contact Sylvain Sardy.
Added on Wednesday, 3 May 2000
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- Estimating the smoothing parameter in wavelet denoising
To estimate a noisy signal with WaveShrink (a wavelet-based
non-parametric estimator) a crucial step is the selection of
the smoothing parameter. Many techniques have been developped amoung
which minimax, cross validation and SURE. I have a fairly simple idea
that looks promissing based on the simulations I made. If you want
to do some mathematical derivations to develop this new technique
and do some computer simulations to see how it works in practice, let me
know.
Requirements: interest in the area of smoothing (function estimation
from noisy data); programming skills; basic knowledge of statistics;
motivation.
If you want further information, please contact Sylvain Sardy.
Added on Tuesday, 18 January 2000
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