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Complex real-time embedded systems require guarantees regarding the assurance of their timing requirements. Such guarantees can be derived using advanced design and analysis methods. Many design solutions address the complexity of these systems using component-based techniques. In this paper we focus on resource sharing in component-based systems with several components executing on a multi-core processor. We consider that the tasks of each component can be scheduled on any core with the possibility of two tasks belonging to the same component executing in parallel. We propose the Parallel Hierarchical Resource Policy, a novel resource sharing policy for multi-core component-based systems. We also develop a detailed response-time based schedulability analysis for the individual components and for the composed system, assuming that intra- and inter-component resource sharing takes place.