Oscar Peralta Gutierrez: Modelling of complex stochastic systems is usually a trade–off between the specification of a sufficient general mathematical model and downgrading to what is feasible from an analytical, numerical or statistical point of view.
The class of phase–type distributions has successfully been employed in a variety of stochastic models since they allow for either explicit or numerically exact solutions. The specification of phase–type distributions in more complex continuous time stochastic processes is new and will be pursued in my PhD study. This includes the study of Parisian ruin for general risk models, time-average calculations of risk models, risk processes with heavy tailed claims, and multivariate risk models.
Supervisors: Bo Friis Nielsen and Mogens Bladt
Published as report: Advances of matrix–analytic methods in risk modelling