Fractional Distributions and Stochastic Processes with Applications

The formulation of flexible and at the same time parsimonious models for stochastic phenomena is a crucial ingredient in the process of managing risks in various application areas of operations research.
In this context, Kulkarni class of phase-type distributions has been proven to have significant modelling advantages and applications. In this project we will consider extensions of fractional Phase-type distributions and construction of counting processes where the inter-arrival times have the aforementioned distribution. Fractional phase-type distributions allow to model the tail dependence which is a particular concern in insurance mathematics, especially for when heavy tailed phenomena occur.
Applications of this process in the context of insurance will be considered. Additionally, further extensions from fractional phase types to fractional Markov arrival processes and their applications would be considered.