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
Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliabili ....Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliability, finance and insurance, were accurate simulation techniques are becoming increasingly important.Read moreRead less
Stochastic analysis and the development and application of financial risk processes. Ensuring the stability of Australia's financial system requires an understanding of the complex financial instruments, strategies and technologies that have evolved in recent years. A strong well-integrated research effort in stochastic analysis with particular application to financial markets is fundamental for measuring and managing risk, to protect and preserve a well functioning system, and to inform policy ....Stochastic analysis and the development and application of financial risk processes. Ensuring the stability of Australia's financial system requires an understanding of the complex financial instruments, strategies and technologies that have evolved in recent years. A strong well-integrated research effort in stochastic analysis with particular application to financial markets is fundamental for measuring and managing risk, to protect and preserve a well functioning system, and to inform policy debate on financial strategies and insurance liabilities.
These challenges are global and require extensive international research collaboration and interaction. The present project will enhance Australia's contributions in this area and facilitate its global impact more than is possible through individual efforts.Read moreRead less