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
G-expectation and its applications to nonlinear risk management. This project will develop novel theories and methods for nonlinear risk management based on nonlinear expectations and Backward Stochastic Differential Equations. The expected outcomes of the project will place Australia in the forefront and the leading position of these fields.
Multiscale Singularly Perturbed Control Systems. We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were ....Multiscale Singularly Perturbed Control Systems. We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were frozen, possesses certain ergodicity properties expressed in the existence of its limit occupational measures set. Conditions for the existence of such a set will be studied and its structure will be described.Read moreRead less
Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems. Problems of control of nonlinear dynamical systems attract continued interest of eminent researchers motivated by important applications and by the fact that analytical and/or numerical analysis of a general nonlinear control problem presents a challenging task. The outcomes of the project will be both fundamental theoretical re ....Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems. Problems of control of nonlinear dynamical systems attract continued interest of eminent researchers motivated by important applications and by the fact that analytical and/or numerical analysis of a general nonlinear control problem presents a challenging task. The outcomes of the project will be both fundamental theoretical results and readily applicable (linear programming based) algorithms that will equip researchers and engineers with new tools for analysis and numerical solution of nonlinear control problems (including problems that have been intractable so far). The project will further enhance Australia's international reputation in Control Theory and its Applications.
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Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems. Problems of optimal control of long-run average and singularly perturbed systems arise in many applications. The project will lead to the development of new linear programming based techniques for analyzing these problems (including problems intractable so far) and finding their numerical solutions. The new techniques will have a potential to be further developed into software that can benefit A ....Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems. Problems of optimal control of long-run average and singularly perturbed systems arise in many applications. The project will lead to the development of new linear programming based techniques for analyzing these problems (including problems intractable so far) and finding their numerical solutions. The new techniques will have a potential to be further developed into software that can benefit Australian industries and technologies. The proposed topic is in the focus of interest of many eminent researchers around the world and the dissemination of our results will further improve Australia's standing in the international research community. Read moreRead less
Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis. The proposed research will significantly advance knowledge by creating new analytical and numerical methods for tackling complex nonlinear control problems arising in many applications. The study's outputs will lead to a deeper understanding of fundamental issues in mathematical modelling. Collaboration with renowned researchers will further improve Australia's st ....Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis. The proposed research will significantly advance knowledge by creating new analytical and numerical methods for tackling complex nonlinear control problems arising in many applications. The study's outputs will lead to a deeper understanding of fundamental issues in mathematical modelling. Collaboration with renowned researchers will further improve Australia's standing in the international research community. Also their visits may further promote research both within and outside the host institution. In particular, lectures and seminars that they will deliver will be transmitted to Australian universities participating in the Access Grid Room Project.Read moreRead less
Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of internation ....Communication and information storage mechanisms in complex dynamical brain networks. Recordings of electrical activity in the brain often cycle repetitively. The aim of this research is to explain how these brain rhythms assist the brain to coordinate simultaneous activity in several regions. Australian socioeconomic benefits include: (i) contributions to the knowledge base of theoretical neuroscience, enhancing Australia's reputation for cutting-edge research; (ii) strengthening of international collaborations with Europe and Japan; (iii) outcomes will ultimately impact on improved medical bionics and future interfaces between brain activity and machines or computers; and (iv) commercialization and technology transfer opportunities, via the transfer of results to biologically inspired engineering.Read moreRead less
Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analy ....Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.Read moreRead less
Dynamic risk measures. Exposure to risk is a pervasive problem. The results will be of importance for financial institutions when they estimate their exposure to risk. Other applications will be to determine the level of risk from a terrorist attack or regional instability. Companies wish to allocate resources to minimize their exposure to adverse events.
Root-to-shoot: modeling the salt stress response of a plant vascular system. Salt and drought are the two major abiotic stresses affecting crop plant health, growth and development. We aim to understand salt and water transport in plants and the physiological effects of soil salinity. Using biophysical models, we will quantify the movement of salt through plant organs, tissues and cells, from root to leaf. We aim to answer the question of how salt moves across the different tissues and major org ....Root-to-shoot: modeling the salt stress response of a plant vascular system. Salt and drought are the two major abiotic stresses affecting crop plant health, growth and development. We aim to understand salt and water transport in plants and the physiological effects of soil salinity. Using biophysical models, we will quantify the movement of salt through plant organs, tissues and cells, from root to leaf. We aim to answer the question of how salt moves across the different tissues and major organs, how salt accumulates in root, leaf and shoot cells, and how movement and accumulation is controlled by the diversity of transport mechanisms operating in plants. We aim to quantify tissue tolerance, osmotic tolerance and ionic tolerance and discover new mechanisms by which plants can stave off the effect of salt stress.Read moreRead less