In this paper, we describe assumptions and assertions needed to account for continuity and availability risks in Advance Receiver Autonomous Integrity Monitoring (ARAIM). We identify key differences with current RAIM-based operations, including the potential of ARAIM to not require systematic pre-flight availability screening. The assumptions and assertions provide a rationale on why fault exclusion is needed in horizontal-ARAIM (H-ARAIM), but is not needed in vertical ARAIM (V-ARAIM). We implement existing methods and design new approaches to predict continuity and availability in the presence of satellite faults and outages, and we analyze performance sensitivity to risk requirements and measurement models.