| The most natural stochastic models for describing the time evolution of the collective risk reserves of an insurance company are jump or point process models. However, there are difficulties in obtaining from such models explicit and tractable expressions for important quantities such as the probability of ruin and these have spawned the development of procedures to approximate point process models. In this thesis, the nature of weak approximations, as put forward by Iglehart (1969) and Furrer, Michna & Weron (1996), is examined closely with a view toward assessing their value. An interpretation of these approximation procedures is given and a method by which the value of weak approximations may be improved is suggested by considering their Levy-Grigelionis-Jacod characteristics. |
