Maximum likelihood estimation of the parameters of stochastic differential equations. The primary objective of this project is to develop efficient algorithms for estimating the parameters of stochastic differential equations (SDEs) by simulated and exact maximum likelihood. The research will draw on both parametric and non-parametric analysis in novel ways to construct estimation procedures that are computationally feasible. These methods will then be applied in the area of finance and used to ....Maximum likelihood estimation of the parameters of stochastic differential equations. The primary objective of this project is to develop efficient algorithms for estimating the parameters of stochastic differential equations (SDEs) by simulated and exact maximum likelihood. The research will draw on both parametric and non-parametric analysis in novel ways to construct estimation procedures that are computationally feasible. These methods will then be applied in the area of finance and used to estimate the parameters of stochastic-volatility models, thus contributing to knowledge in a prominent area of complex systems, namely financial risk. The execution of this collaborative project will deliver quality research training in the topical area of mathematical finance and produce high-calibre postgraduates.
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Modelling Hidden Processes which Drive Economic and Financial Systems. The ability to forecast complex economic systems is crucial to benefit from peak performance, and to prepare for and safeguard against downturn. This project aims to make significant discoveries concerning hidden processes which drive such systems, using rigorous, cutting-edge, flexible econometric methods. Resulting outcomes will be improved understanding of - and ability to forecast - important economic phenomena such as vo ....Modelling Hidden Processes which Drive Economic and Financial Systems. The ability to forecast complex economic systems is crucial to benefit from peak performance, and to prepare for and safeguard against downturn. This project aims to make significant discoveries concerning hidden processes which drive such systems, using rigorous, cutting-edge, flexible econometric methods. Resulting outcomes will be improved understanding of - and ability to forecast - important economic phenomena such as volatility in price series, extremal (risky) behaviour of financial systems, and turning points of the business cycle. Discoveries will be disseminated through published papers and presentations at a major international conference. Ongoing e-research links with France will also be established.Read moreRead less
Financial Instability and Risk Management: New Statistical Treatment of the Occurrence and Persistence of Shocks in International Markets. Global economies are complex systems: their complexity is increasing due to market connectivity, borderless trading and rapid electronic transactions. This collaboration will improve understanding of market interdependence, important because of its profound macroeconomic influence on individual consumersf decisions and corporate investment. A novel combinati ....Financial Instability and Risk Management: New Statistical Treatment of the Occurrence and Persistence of Shocks in International Markets. Global economies are complex systems: their complexity is increasing due to market connectivity, borderless trading and rapid electronic transactions. This collaboration will improve understanding of market interdependence, important because of its profound macroeconomic influence on individual consumersf decisions and corporate investment. A novel combination of nonlinear time series and dynamical systems theories will be used to describe propagation and persistence of market shocks. Focusing on smart information use and innovation economies, this project will deliver publications on new practical econometric methodologies, training for early career researchers, and a strong sustainable research relationship between Australia and France.Read moreRead less
International Networks in Applied Bayesian Statistics: improving Australia''s knowledge through intelligent data analysis and modelling. National benefits of this project are fourfold: (i) new international networks between Australia, Southern Africa, France and USA in the priority area of mathematical sciences; (ii) state-of-the-art Bayesian statistical methods for integrating and analyzing non-standard data and diverse information sources, including expert opinion, in order to solve complex pr ....International Networks in Applied Bayesian Statistics: improving Australia''s knowledge through intelligent data analysis and modelling. National benefits of this project are fourfold: (i) new international networks between Australia, Southern Africa, France and USA in the priority area of mathematical sciences; (ii) state-of-the-art Bayesian statistical methods for integrating and analyzing non-standard data and diverse information sources, including expert opinion, in order to solve complex problems in environment, industry, health, defence; (iii) direct contribution to solution of global environmental problems, specifically water quality, threatened species and environmental risk; (iv) superior training of the next generation of the global community of researchers in applied statistics.Read moreRead less
Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also ....Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also applicable to microscopic systems. The expressions will determine the probability that finite sized systems will violate the Second Law for small periods of time and will therefore contribute to development of a fundamental understanding of microscopic systems and the development of nanotechnology.
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Peripheral aberrations of the human eye. This project will benefit Australia from several perspectives. It will make an important contribution to understanding limitations to peripheral vision of the eye, particularly as a result of refractive surgical intervention. This is important because many Australians will require such surgery. Being able to better measure and correct peripheral aberrations will lead to improved imaging of the eye and thus contribute to improved detection and diagnosis of ....Peripheral aberrations of the human eye. This project will benefit Australia from several perspectives. It will make an important contribution to understanding limitations to peripheral vision of the eye, particularly as a result of refractive surgical intervention. This is important because many Australians will require such surgery. Being able to better measure and correct peripheral aberrations will lead to improved imaging of the eye and thus contribute to improved detection and diagnosis of ophthalmic disease. The study will benefit ophthalmologists, optometrists, and engineers involved in designing visual instruments. This project will provide training in adaptive optics for graduate students not available in any other Australian institution.Read moreRead less
Raman spectroscopy and imaging of natural and synthetic melanins. The national benefit of this research lies in three main areas. First, this research could lead to a non-invasive diagnostic for melanoma. Second, it could reveal stronger connections between melanin and melanoma development than previously believed and thus inspire possible methods of treatment or prevention of melanoma. Given Australia's high incidence of melanoma, these could have an enormous impact on our health care system. T ....Raman spectroscopy and imaging of natural and synthetic melanins. The national benefit of this research lies in three main areas. First, this research could lead to a non-invasive diagnostic for melanoma. Second, it could reveal stronger connections between melanin and melanoma development than previously believed and thus inspire possible methods of treatment or prevention of melanoma. Given Australia's high incidence of melanoma, these could have an enormous impact on our health care system. Third, it will increase our understanding of the melanin pigment and further establish Australia as a leader in this field. Given the links between melanin and Parkinson's Disease and immune response, this understanding could have greater impact on health care than simply melanoma.Read moreRead less
The kinematics of the anterior eye deformation. This project has a potential to benefit Australia from a number of perspectives. The outcomes will provide ophthalmologists and optometrists with currently unavailable knowledge on dynamic behaviour of eye. In particular the research will identify aspects of corneal deformation that in turn will help improve the accuracy of refractive surgeries and aid in the management of glaucoma. Also, the knowledge generated through this project will be of valu ....The kinematics of the anterior eye deformation. This project has a potential to benefit Australia from a number of perspectives. The outcomes will provide ophthalmologists and optometrists with currently unavailable knowledge on dynamic behaviour of eye. In particular the research will identify aspects of corneal deformation that in turn will help improve the accuracy of refractive surgeries and aid in the management of glaucoma. Also, the knowledge generated through this project will be of value to engineers designing advanced clinical instrument for measuring eye parameters. Read moreRead less