Driving behavior modeling is an essential component of Advanced Driver Assistance Systems (ADAS). Existing methods usually analyze driving behaviors based on generic driving data, which do not consider personalization and user privacy. In this paper, we propose pBEAM, a collaborative cloud-edge computation system for personalized driving behavior modeling. The driving behavior model is built on top of Generative Adversarial Recurrent Neural Networks (GARNN), which adapts to the dynamic change of normal driving. Transfer learning from cloud to edge improves the model performance and robustness on the edge. We prune the deep neural networks in the cloud in order to minimize the model transferring load while maximally preserve the original model performance. A personalized edge model is trained on top of the pruned model using CGARNN-Edge (Conditional GARNN), which considers drivers' personal or contextual information as additional conditions. User privacy is well protected as no personal data needs to be uploaded to the cloud. Experimental results on driving data from both real world and driving simulator show that the proposed CGARNN-Edge achieves the best performance among all the methods.