Agentic AI for Commercial Insurance Underwriting with Adversarial Self-Critique

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.

Artificial intelligence (AI) is beginning to reshape actuarial practice, particularly in domains that require reasoning over unstructured documents, heterogeneous data sources, and regulated decision workflows. Actuaries now face a design space that ranges from traditional rule-based automation to large language models (LLMs), retrieval-augmented generation (RAG), and multi-agent agentic'' systems that plan, retrieve, call tools, and reflect. This paper examines how these emerging architectures can support actuarial priorities such as transparency, auditability, and human-in-the-loop governance, with a focus on straight-through decision processes. To make these ideas concrete, we develop and analyze an agentic AI framework for straight-through underwriting of small commercial Business Owner Policies (BOPs). We construct a synthetic but realistic experimental environment and compare three underwriting pipelines: (i) a single-LLM baseline, (ii) a naive RAG system, and (iii) a multi-agent Agentic RAG'' pipeline that combines targeted retrieval, third-party data checks, and explicit multi-step rule evaluation. The agentic system performs best overall, with the largest gains in multi-step and missing-information scenarios, where structured retrieval and reflection help the model avoid unsupported straight-through decisions.

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.