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Boundary Crossing Analysis for Random Processes with Applications to Risk Management

Funding: 2008: $80,000
2009: $80,000
2010: $75,000

Project Member(s): Novikov, A., Craddock, M.

Funding or Partner Organisation: Australian Research Council (ARC Discovery Projects)

Start year: 2008

Summary: Solving a number of important applied problems requires finding the probability that a random process crosses some boundary. Problems of this kind arise in many applications related to environmental and financial risk management, insurance, stochastic control of systems etc. The project aims to develop new analytical and computational methods for evaluating distributions and other characteristics related to boundary crossing events. The models we will work with include jump-diffusion processes evolving in random environments. Potential applications to defaultable derivatives in finance and carbon-emission trading schemes, equity-linked contracts in insurance and control charts for security monitoring are within the scope of the project.

Keywords: stochastic boundary functionals, environmental and financial risk, superannuation schemes, changepoint analysis, stochastic differential equations, Markov processes,

FOR Codes: Stochastic Analysis and Modelling, Finance, Risk Theory, Mathematical sciences, Finance and investment services, Insurance services, Financial Mathematics, Expanding Knowledge in the Mathematical Sciences, Superannuation and Insurance Services, Finance Services