Liquidity in financial markets. This project aims to develop a theory which models the effect of liquidity on option prices under different market conditions. Economic or financial crises are inevitable and affect economics. During or after a major financial crisis, market liquidity usually becomes risky and needs to be studied. Through both empirical and theoretical explorations, this project will quantify and measure liquidity risk and its effect on the options markets. It will develop a frame ....Liquidity in financial markets. This project aims to develop a theory which models the effect of liquidity on option prices under different market conditions. Economic or financial crises are inevitable and affect economics. During or after a major financial crisis, market liquidity usually becomes risky and needs to be studied. Through both empirical and theoretical explorations, this project will quantify and measure liquidity risk and its effect on the options markets. It will develop a framework to help market regulators manage illiquidity, enhance the efficiency of option trading in illiquid markets and help in the detection of market manipulation.Read moreRead less
Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and ....Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and the economy. This project expects to bring about long-term impact on quantitative finance and related applications through providing a deep understanding of, and a new perspective for, the design, risk and fairness of the finance, property and insurance markets.Read moreRead less
G-expectation and its applications to nonlinear risk management. This project will develop novel theories and methods for nonlinear risk management based on nonlinear expectations and Backward Stochastic Differential Equations. The expected outcomes of the project will place Australia in the forefront and the leading position of these fields.
New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include po ....New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include powerful and reliable mathematical models ready for application, and national and international collaborations with scientists and mathematicians. This should provide significant benefits including increased capacity to use mathematical models in vascular biology and training young researchers in interdisciplinary methods.Read moreRead less
Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-struct ....Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-structural domains. Dealing with this mathematical complexity is critical to developing high efficiency energy generation and gas storage systems. This is expected to enhance transport mechanisms within electrochemical devices and create opportunities for industry to use electrofunctional materials.Read moreRead less
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software ....New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software implementations. Both nonsmooth and integer optimisation problems have a good mathematical basis, but there are "gaps"; existing methods cannot always solve real industrial problems. This project will deliver better methods, built on better theory, and so will yield better solutions for important applications.Read moreRead less
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.Read moreRead less
Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less