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
Three-dimensional Bayesian Modelling of Geological and Geophysical data. The project aims to develop technologies enabling rapid informed decision-making related to the management of natural resources, including critical metals, copper and water. This new technology will support a greener future, securing our energy future, our access to clean water and reduce the mining footprint. Expected outcomes include an enhanced capability in interoperable, integrated three-dimensional geological and geop ....Three-dimensional Bayesian Modelling of Geological and Geophysical data. The project aims to develop technologies enabling rapid informed decision-making related to the management of natural resources, including critical metals, copper and water. This new technology will support a greener future, securing our energy future, our access to clean water and reduce the mining footprint. Expected outcomes include an enhanced capability in interoperable, integrated three-dimensional geological and geophysical modelling in order to predictively characterise sub-surface geology. The outcome will be an open-source forecasting dashboard enabling decision making while considering underlying risk related to resource extractions and management with significant benefits to the Australian society (lower emissions, clean water).Read moreRead less
Enabling three dimensional stochastic geological modelling. This project aims to develop technologies to mitigate three dimensional (3D) geological risk in resources management. This project expects to create new knowledge and methods in the field of 3D geological modelling through the innovative application of mathematical methods, structural geology concepts and probabilistic programming. The expected outcomes are an enhanced capability to model the subsurface, characterise model uncertainty a ....Enabling three dimensional stochastic geological modelling. This project aims to develop technologies to mitigate three dimensional (3D) geological risk in resources management. This project expects to create new knowledge and methods in the field of 3D geological modelling through the innovative application of mathematical methods, structural geology concepts and probabilistic programming. The expected outcomes are an enhanced capability to model the subsurface, characterise model uncertainty and test multiple geological scenarios. This enhanced capability is important for the future of Australia's subsurface management, including urban geology and our continuously growing sustainable resources industry.Read moreRead less
Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the ....Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the outstanding performance of our Snakes-and-Ladders Heuristic (SLH) for the solution of the Hamiltonian cycle problem to identify its "fixed complexity orbits" and generalise this notion to other NP-complete problems.Read moreRead less