Abstract

The family of phase-type (PH) distributions has many good properties such as closure under convolution and mixtures and have rational Laplace transforms. PH distributions are widely used in applications of stochastic models such as in queueing systems, biostatistics and engineering. They are also applied to insurance risk. In this thesis, we discuss the moment generating function (m.g.f.) of a compound present value risk process with phase-type (PH) deflated claim severities under a net interest e = 0. This represents a generalization of the classical risk model e = 0. A closed form of the m.g.f. of a compound Poisson present value risk process with PH deflated claims is obtained. We also consider the discounted compound renewal process and get homogeneous differential equations for its m.g.f. in the case of PH deflated claims. Applications and some numerical examples are given to illustrate the results.