Verifiably Autonomous: Formal Verification of Autonomous AI Agent Decision Chains in Zero Trust Financial Risk and Fraud Environments

As autonomous artificial intelligence (AI) agents transition from passive credit scoring and fraud classification to executing multi-step decision chains in safety-critical financial environments—such as high-frequency algorithmic market making, automated anti-money laundering (AML) asset freezing, cross-border settlement, and dynamic liquidity management—ensuring high precision alongside absolute risk compliance becomes paramount. Traditional statistical validation, backtesting, and empirical stress-testing fall short when confronting the inherent opacity, non-determinism, and infinite state spaces of generative models and deep neural controllers. A single hallucinated transaction parameter set, unauthorized logic branch, or out-of-distribution execution can trigger systemic market instability, severe regulatory non-compliance, or irreversible capital destruction. This paper presents a novel Financial Hybrid Verification Architecture (Fin-HVA) designed to mathematically certify the correctness, policy compliance, and risk bounds of autonomous agent decision sequences prior to market execution. We introduce a neuro-symbolic semantic parser that converts complex natural language reasoning and tool-use parameter arrays into formal Linear Temporal Logic (LTL) formulas and Satisfiability Modulo Theories (SMT) queries. By coupling static SMT reachability solvers with a real-time Runtime Financial Safety Shield (RFSS) and an autonomous evaluator-optimizer repair loop, Fin-HVA guarantees that agent decisions remain strictly bounded within predefined risk envelopes (e.g., maximum drawdown thresholds, capital adequacy ratios, and regulatory compliance constraints). We evaluate Fin-HVA across three simulated high-risk financial domains: automated high-frequency algorithmic liquidity management, dynamic credit line adjustment, and real-time AML transaction interdiction. Our experimental results demonstrate that Fin-HVA completely eliminates safety and compliance violations (0.0% Violation Rate) while maintaining high operational task success rates (>94%) with negligible step latency (<1.3s). This research establishes a rigorous mathematical foundation for deploying fully autonomous AI agents within highly regulated financial ecosystems.