Agentic AI introduces new insurance challenges because autonomous AI systems can make decisions, invoke tools, modify external environments, and interact with third-party services. This paper develops an AI-native mathematical framework for underwriting, pricing, and contract design for agentic AI deployments. A deployment is represented by a risk state that captures autonomy level, operational authority, permission exposure, governance maturity, and dependency concentration. The framework maps the risk state to event probabilities, loss severities, governance costs, premiums, deductibles, coverage allocation, and policy covenants, and formulates an optimization problem for insurance contract design under participation, profitability, and incentive compatibility constraints. The paper establishes structural properties of insurability, including characterization of an insurability region, monotone deterioration of feasibility with increasing exposure, and governance certification thresholds. Insurance is further interpreted as both an operational cost and a regulatory mechanism for AI deployment. A healthcare case study illustrates contract optimization, sensitivity analysis, and automated claims processing for agentic AI systems.
AI agents can now take irreversible actions in operational systems, but agent-caused losses are still not clearly assigned, priced, or transferred. Providers often disclaim consequential damages, users are left with uncompensated losses, and default human review limits the efficiency gains of automation. We ask when autonomous AI deployment can become economically acceptable despite failure risk. Our answer is to quantify risk at the customer-task-trace episode level and transfer it through insurance. Automation is acceptable when its expected benefit exceeds the premium, control cost, and remaining risk. This requires a defined role with bounded permissions and comparable traces. We introduce trace-economic underwriting, which maps tool-use traces to customer exposure and claimable loss, then uses this representation for pricing, control, and risk transfer. It uses deterministic economic labels rather than an LLM judge. In our trace-to-loss testbed, trace-economic pricing reduces pricing MAE from $17.7K to $569 and removes regressive cross-subsidy. A 300-trace expert audit accepts 295 labels unchanged. On 1,000 real SWE-smith traces, trace-conditioned controls reduce CVaR95 by 72%. Theorem~1 gives a finite-sample scope condition. We release code, labels, and audit sheets.
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.