Large Language Models (LLMs) and Large Reasoning Models (LRMs) offer transformative potential for high-stakes domains like finance and law, but their tendency to hallucinate, generating factually incorrect or unsupported content, poses a critical reliability risk. This paper introduces a comprehensive operational framework for hallucination management, built on a continuous improvement cycle driven by root cause awareness. We categorize hallucination sources into model, data, and context-related factors, allowing targeted interventions over generic fixes. The framework integrates multi-faceted detection methods (e.g., uncertainty estimation, reasoning consistency) with stratified mitigation strategies (e.g., knowledge grounding, confidence calibration). We demonstrate its application through a tiered architecture and a financial data extraction case study, where model, context, and data tiers form a closed feedback loop for progressive reliability enhancement. This approach provides a systematic, scalable methodology for building trustworthy generative AI systems in regulated environments.