Description: This is the abstract of a preliminary report on a research project about the applications of dynamical systems theory in actuarial science. The project is funded by the AERF. The paper will briefly describe the nature of dynamical systems and present a tentative model derived from percolation theory that could be used to understand the pricing variations encountered in a competitive environment and that could also be used as a model for credibility. From Actuarial Research Clearing House 1992, Vol. 1.