A model of earthquake occurrence is proposed that is based on results of statistical studies of earthquake catalogs. We assume that each earthquake generates additional shocks with a probability that depends on time as t-(1+ϑ). This assumption together with one regarding the independence of branching events on adjacent branches of the event 'tree,' is sufficient to permit the generation of complete catalogs of earthquakes that have the same time-magnitude statistical properties as real earthquake catalogs. If ϑ is about 0.5, the process generates sequences that have statistical properties similar to those for shallow earthquakes: many well-known relations are reproduced including the magnitude-frequency law, Omori's law of the rate of aftershock and foreshock occurrence, the duration of a recorded seismic event versus its magnitude, the self-similarity or lack of scale of rate of earthquake occurrence in different magnitude ranges, etc. A value of ϑ closer to 0.8 or 0.9 seems to simulate the statistical properties of the occurrence of intermediate and deep shocks. A formula for seismic risk prediction is proposed, and the implications of the model for risk evaluation are outlined. The possibilities of the determination of long-term risk from real or synthetic catalogs that have the property of self-similarity are dim.