Ideas for MSc projects
Here are some outline ideas for computational projects for the
MSc in Mathematical and Computational Finance (MCF) or
Mathematical Modelling and Scientific Computing (MMSC).
MLMC refers to Multilevel Monte Carlo, for which I have many references
available from
https://people.maths.ox.ac.uk/gilesm/mlmc.html
and
https://people.maths.ox.ac.uk/gilesm/mlmc_community.html
These projects are all best suited to students with solid programming skills
in either python or C/C++. I can assist any students who are interested in
improving their C/C++ skills by using OpenMP for multi-threaded parallelisation
on CPUs, or CUDA for many-threaded paralleisation on GPUs.
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Use of adjoints for the efficient estimation of Greeks, in the context of
a) finite difference methods; b) Monte Carlo simulations (MCF)
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Use of MLMC branching path simulations
(see arXiv paper)
to reduce variance of
a) bumping for Greeks, especially for digitals;
b) pathwise Greeks (combining ideas from this arXiv paper);
c) CDF estimation (MCF)
-
MLMC change of measure for complex digital options, as suggested in
my MCQMC12 review paper
on multilevel Monte Carlo methods, but not yet tried.
(MCF)
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MLMC for stochastic PDEs (MMSC)
-
MLMC for randomised Numerical Linear Algebra, possibly jointly supervised
by Prof Yuji Nakatsukasa (MMSC)
-
A topic in High Performance Computing, using OpenMP on CPUs or CUDA on GPUs,
perhaps as part of a project with another supervisor. I have some specific
ideas for CUDA projects, but they would need someone with very strong
programming skills who is interested in immersing themselves in the
challenges of parallel programming on GPUs (MMSC)