Following calls to advance the integration of risk and business process modeling paradigms, this paper formalizes the process of incorporating risk into business process models through the principles of Value-Focused Process Engineering (VFPE). In doing so, the paper aims to extend the existing VFPE modeling notation to reflect a set of necessary constructs required to adequately represent risk in goal-oriented business-process models. The extended set of constructs is proposed to support a formal systems view of process-based risk. Process-based risk is formalized on the one hand, as a product of complex interactions between activity-based elements, and on the other hand, as a natural component of the value creation mechanism of an elementary function or a complex process. The proposed risk-aware VFPE formalism also formulates rules for decomposing risk in process models according to the organizational values, thereby enabling better risk visibility, reducing process complexity, and ensuring continuity of business processes.