Market Model of Implied Volatility. The outcomes of the project will constitute a new methodology with a wide range of tools to handle the market uncertainties with practical applications in the finance industry. Consequently, the benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of modelling of complex stochastic systems and the benefits resulting from its commercially rele ....Market Model of Implied Volatility. The outcomes of the project will constitute a new methodology with a wide range of tools to handle the market uncertainties with practical applications in the finance industry. Consequently, the benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of modelling of complex stochastic systems and the benefits resulting from its commercially relevant elements. Read moreRead less
New models and valuation methods for portfolio credit derivatives. Portfolio credit derivatives provide a mechanism to simultaneously transfer credit exposures to a large number of counterparties within a single transaction. However, no generally accepted valuation model for such credit portfolios is currently available. This project aims to develop new mathematically-based technologies to allow institutions such as Westpac (the Industry Partner) to optimally manage their credit exposures. The o ....New models and valuation methods for portfolio credit derivatives. Portfolio credit derivatives provide a mechanism to simultaneously transfer credit exposures to a large number of counterparties within a single transaction. However, no generally accepted valuation model for such credit portfolios is currently available. This project aims to develop new mathematically-based technologies to allow institutions such as Westpac (the Industry Partner) to optimally manage their credit exposures. The outcome will be a class of superior models and operational risk management tools that will ensure the value and risks of these transactions are properly understood and accurately quantified. These models will enhance both the knowledge base of the industry and academic scholarship.
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A Principled Approach to Computer Simulation of Dynamic General Equilibrium Macroeconomic Models. In the last two decades a new generation of computer-intensive
modeling techniques has risen to prominence in macroeconomics. These
methods have broad policy applications, from public finance and
reserve bank operation to analysis of long-run productivity growth,
taxation reform, unemployment, international trade policy and natural
resource conservation. The size and complexity of these model ....A Principled Approach to Computer Simulation of Dynamic General Equilibrium Macroeconomic Models. In the last two decades a new generation of computer-intensive
modeling techniques has risen to prominence in macroeconomics. These
methods have broad policy applications, from public finance and
reserve bank operation to analysis of long-run productivity growth,
taxation reform, unemployment, international trade policy and natural
resource conservation. The size and complexity of these models means
that even computer-based techniques will rely for the foreseeable
future on efficient program design to solve them. The project will
construct a comprehensive set of solution techniques and software for
this class of macroeconomic models, including detailed mathematical
analysis on accuracy of model output.Read moreRead less
Water derivatives: conceptualisation, price modelling and economic impacts. Introducing water options is likely to provide farmers with more choices on trading their water allocation and enhance water price certainty. Recent seasons have accentuated the potential benefit of water options: regions with highly secure water in the past have suffered repeated shortfalls in allocations. Water options would alter the behaviour of water managers who would need to ensure sufficient carryover to future s ....Water derivatives: conceptualisation, price modelling and economic impacts. Introducing water options is likely to provide farmers with more choices on trading their water allocation and enhance water price certainty. Recent seasons have accentuated the potential benefit of water options: regions with highly secure water in the past have suffered repeated shortfalls in allocations. Water options would alter the behaviour of water managers who would need to ensure sufficient carryover to future seasons to allow for drought. Options markets may improve the allocation of water between competing users. Such markets, by reducing uncertainty, may reduce excessive adjustment costs arising from drought by improving water access security.Read moreRead less
Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamil ....Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamiltonian cycles in a graph. Analysis of the determinant objective function in terms of the eigenvalues may lead to new spectral properties of stochastic matrices. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in a wide range of applications.Read moreRead less
Understanding cycles in mineral commodity price, a market model with uncertainty. Mining accounts for more than 8% of Australia's GDP, and almost 50% of Australia's total merchandise exports. Understanding phenomenological mechanisms for price fluctuations and using our dynamic price model can help determine better timing of investments in mining infrastructure. This knowledge will help Australia benefit from the upside of commodity 'cycles', super or not. The market model that will be develope ....Understanding cycles in mineral commodity price, a market model with uncertainty. Mining accounts for more than 8% of Australia's GDP, and almost 50% of Australia's total merchandise exports. Understanding phenomenological mechanisms for price fluctuations and using our dynamic price model can help determine better timing of investments in mining infrastructure. This knowledge will help Australia benefit from the upside of commodity 'cycles', super or not. The market model that will be developed in this project can be used to assist in better planning for commodity cycle upside, improving the overall efficiency of capital utilisation in the long term.Read moreRead less
Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater a ....Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater aquifers beyond their long-term yield. Large areas of land have been lost to saltwater intrusion. This proposal will provide suitable tools to predict the level and movement of saltwater in the aquifers. Application to the development of management strategies would bring direct benefit to coastal areas where salinity is a sustainability issue.Read moreRead less
Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized ran ....Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized random fields allow us to formulate a comprehensive program to tackle some key problems including modeling, processing and statistical estimation of fractional diffusion. Advances made in this program will in turn benefit the developments in related scientific fields.Read moreRead less
Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the ....Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the fact that Australian institutions will be (in part) responsible for key theoretical results in this growing field will strengthen Australia's position worldwide as an international centre for computer science.Read moreRead less
Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.Read moreRead less