In this paper, we present a formal model, named PobSAM (Policy-based Self-Adaptive Model), for developing and modeling self-adaptive systems. In this model, policies are used as a mechanism to direct and adapt the behavior of self-adaptive systems. A PobSAM model consists of a set of self-managed modules(SMM). An SMM is a collection of autonomous managers and managed actors. Managed actors are dedicated to functional behavior while autonomous managers govern the behavior of managed actors by enforcing suitable policies. To adapt SMM behavior in response to changes, policies governing an SMM are adjusted, i.e., dynamic policies are used to govern and adapt system behavior. We employ the combination of an algebraic formalism and an actor-based model to specify this model formally. Managers are modeled as meta-actors whose policies are described using an algebra. Managed actors are expressed by an actor model. Furthermore, we provide an operational semantics for PobSAM described using labeled transition systems.