Most of the existing approaches to trust management focus on the issues of assessing the trustworthiness of other entities and of establishing trust between entities. This is particularly relevant for dynamic, open and distributed systems, where the identity and intentions of other entities may be uncertain. These approaches offer methods to manage trust, and thereby to manage risk and security. The methods are, however, mostly concerned with trust management from the viewpoint of the trustor, and the issue of mitigating risks to which the trustor is exposed. This paper addresses the important, yet quite neglected, challenge of understanding the risks to which a whole system is exposed, in cases where some of the actors within the system make trust-based decisions. The paper contributes by proposing a method for the modeling and analysis of trust, as well as the identification and evaluation of the associated risks and opportunities. The analysis facilitates the capture of trust policies, the enforcement of which optimizes the trust-based decisions within the system. The method is supported by formal, UML-based languages for the modeling of trust scenarios and for trust policy specification.