Agentic artificial intelligence (AI) systems are transforming the risk landscape by extending beyond information generation to autonomous planning, tool invocation, decision execution, and persistent modification of digital and physical environments. These capabilities introduce novel exposures that do not fit neatly within traditional insurance categories such as cyber, professional liability, product liability, or directors and officers coverage. This paper examines the emerging insurance market for agentic AI and develops a framework for understanding its underwriting, pricing, reinsurance, and product-design implications. We characterize agentic AI as a continuum of autonomy and delegated authority, emphasizing the distinction between informational outputs and systems capable of independently generating insured events through external actions. We analyze major risk pathways, including hallucinations, prompt-injection attacks, autonomous decision errors, model drift, dependency failures, and cyber-physical harms, and evaluate how existing insurance products are adapting to address these exposures. The paper further proposes an actuarial framework based on exposure assessment, scenario analysis, dependency mapping, and accumulation-risk management, drawing parallels to the evolution of cyber insurance. Finally, we present a coordinated insurance architecture that integrates cyber, technology errors and omissions, product liability, performance-warranty, and affirmative AI-liability coverages through explicit allocation mechanisms and dedicated AI aggregates. The analysis suggests that the future of agentic-AI insurance lies not in a single monoline product but in a layered ecosystem of complementary coverages supported by improved governance, transparency, telemetry, and regulatory clarity.