Although P2P systems are usually used for information exchange between peers, they have either protected peers' anonymity, or required transacting peers to trust each other implicitly. Both these approaches are vulnerable to attacks by malicious peers who could abuse the P2P system to spread viruses, incorrect, or damaging information. In this paper, we propose an approach for trust management in P2P systems. We introduce an optimistic role-based model for trust amongst peers and show that it is scalable, dynamic, revocable, secure and transitive. Our proposed solution permits asymmetric trust relationships that can be verified by any peer in the system through a simple, low-cost algorithm. This paper introduces a metric known as iComplex that combines a peer's trust value for each of its roles into a single, relative, probabilistic guarantee of trust. Finally, we discuss how our trust model allows peers to revoke relationships with malicious peers, and the non-repudiation of peer relations. We use simulations to illustrate the trust value distribution amongst peers in the network. Our analysis and experiments demonstrates the low-cost involved to verify and validate trust values. Lastly, we establish the effectiveness of using sum as the aggregation function to combine trust values of a peer.