Research strengths
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Mathematics of RiskFrom observing previous and current financial and other problems it is clear
that risk is a pervasive component of existence for all organizations. What is
perhaps less well known is how mathematics can model exposure and indicate
appropriate steps to reduce loss. Financial risk is only one aspect of the
subject, though at the moment probably the most highly developed mathematically.
Risk arises when companies plan future operations; risk arises when governments
decide policies at the national or international level; indeed, risk arises when
individuals make plans for the future. The essence of risk, indeed of life, is
that the future is unknown. Here mathematics, the study of patterns, can
contribute. Mathematically the future can be modelled by considering, in
simplified frameworks, possible scenarios or future states of the world. These
outcomes can then be assessed using methods from probability and random
processes.
Objectives of the research include:
(1) the development of new risk measures, particularly those related to nonlinear expectations and backward stochastic differential equations,
(2) their implementation in both financial and non financial settings,
(3) the calibration or tuning of the models,
(4) the combining of information from different sources, and
(5) the application of the results to problems provided by industry and government.
While financial risk has, so far, motivated the most sophisticated modelling,
mathematics can contribute to assessing and mitigating the effects of risk in
many situations.
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Stochastic Modelling and OptimisationMuch of human intellectual endeavour is
directed to predicting and modifying the future. Initially this is attempted by
looking for patterns. Sophisticated methods for the study of patterns are
provided by mathematics.
Measurements and data are studied to suggest patterns, which are then modelled
mathematically. The predictions of the models are tested against further
observations and the models used to make decisions and modify future outcomes.
The applications of stochastic, or random, processes in engineering, finance,
biology and many other fields fit this paradigm. In all cases real world
measurements and data provide the foundations for theoretical models. These
models are then explored to make predictions and assist in improved decisions,
whether they are investment strategies, management policies in
telecommunications networks, or potential new avenues for cancer treatment.
We are associated with two groups that specialise in performing contract research and consulting with the defence sector, CDCIN, and the telecommunications sector and general industry,
TRC Mathematical Modelling.
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NanomechanicsThe power of nanotechnology is rooted in its potential to revolutionise technology and industry, including information technology, biotechnology, medicine, aerospace, defence, energy and the environment. In order to fully realise the promise of nanotechnology, all the scientific disciplines must be brought to bear, including mathematics and mathematical modelling which can provide insights into the many novel results that are being reported in the experimental literature every week. In the Nanomechanics Group, we employ mathematical modelling using integral calculus, geometry, the calculus of variations, classical mechanics and many other mathematical techniques in order to understand and explain the unique behaviour of nanoscale systems.
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