New Stochastic Processes with Applications in Finance. This project investigates the properties and the use of two new families of models with applications in Finance, and beyond. It will contribute to the development of fundamental research in mathematics and its applications. The project will produce more realistic financial models that will benefit researchers in this field. This will in turn have a flow on effect to benefit the wider community. The project will provide for postgraduate train ....New Stochastic Processes with Applications in Finance. This project investigates the properties and the use of two new families of models with applications in Finance, and beyond. It will contribute to the development of fundamental research in mathematics and its applications. The project will produce more realistic financial models that will benefit researchers in this field. This will in turn have a flow on effect to benefit the wider community. The project will provide for postgraduate training and international scientific exchange. Overall, the project will strengthen Australia's standing at the forefront of fundamental and applied research.Read moreRead less
Boundary Crossing Analysis for Random Processes with Applications to Risk Management. Effective management of environmental, financial and superannuation investment risks is vitally important for Australia. Results of the project will add to the theoretical foundations of risk management and provide new computational tools for specialists working in the areas of financial engineering, insurance, superannuation funds. These tools will assist in improving risk profile evaluation and developing new ....Boundary Crossing Analysis for Random Processes with Applications to Risk Management. Effective management of environmental, financial and superannuation investment risks is vitally important for Australia. Results of the project will add to the theoretical foundations of risk management and provide new computational tools for specialists working in the areas of financial engineering, insurance, superannuation funds. These tools will assist in improving risk profile evaluation and developing new statistical control charts for security monitoring of epidemics, networks intrusions and other potentially dangerous changes. The research will also give Australia a competitive advantage in the area of education related to stochastic processes, mathematical finance, control theory and their applications.Read moreRead less
Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far re ....Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far reaching benefits both nationally and internationally and will allow Australia to strengthen its position in international research. The project will also provide for postgraduate training and international scientific exchange.Read moreRead less
Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Sto ....Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Stochastic Volatility in Finance. The answers to these questions will underpin the statistical theory for potential breakthroughs in the respective areas. This project will contribute to the theory and applications of Stochastic Processes, as well as modelling in biology and finance.Read moreRead less
Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on elec ....Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on electricity futures. Therefore a specific model is needed that takes into account the pricing principle of "no-arbitrage" and combines it with other factors that drive electricity prices. The novel element in this proposal is incorporation of the weather forecasts into the models for electricity options. As a result of this study appropriate models for electricity derivatives for various geographical regions in Australia will be developed.Read moreRead less
Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
Interrogation and estimation of differential equation networks. Complex networks occur in many physical processes, in bridges and buildings and in small nanoscale systems like carbon nanotubes. Similar systems arise in electronics, photonics, and social networks. This project aims to determine optimal measurement regimes to estimate their dynamical states, and to find the limits of that estimation process.
Self-Interacting Random Walks. This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field o ....Self-Interacting Random Walks. This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field of reinforced random walks, and the development of novel methods for their study. This should provide significant benefits not only to the field of mathematics, but also to the myriad of applied disciplines where self-interacting processes are utilised.Read moreRead less
The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype ....The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype-phenotype relationships from family data and the estimation of animal abundance from capture-recapture data. The methods will be applied to real data and their theoretical properties developed. The practical significance of the project is the flexible new statistical methods that will become available to researchers. The theoretical significance will be the insights into semiparametric methods gained by developing these nonstandard applications. The expected outcomes are the new statistical procedures and the resulting theoretical insights into semiparametric statistics.Read moreRead less
Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial the ....Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial theory to name a few. These structures will be further developed, leading to the analytic form of distribution functions quantifying classes of complex systems. Analogous statistical quantification is the essence of recently proposed methods to analyze artificial complex systems such as the stock market.Read moreRead less