Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for ....Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for example, environment risk, climate change, and energy and security problems.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
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less