Automated negotiations in insurance and business-to-business (B2B) commerce encounter substantial challenges. Current systems force a trade-off between convenience and privacy by routing sensitive financial data through centralized servers, increasing security risks, and diminishing user trust. This study introduces a device-native autonomous Agentic AI system for privacy-preserving negotiations. The proposed system operates exclusively on user hardware, enabling real-time bargaining while maintaining sensitive constraints locally. It integrates zero-knowledge proofs to ensure privacy and employs distilled world models to support advanced on-device reasoning. The architecture incorporates six technical components within an Agentic AI workflow. Agents autonomously plan negotiation strategies, conduct secure multi-party bargaining, and generate cryptographic audit trails without exposing user data to external servers. The system is evaluated in insurance and B2B procurement scenarios across diverse device configurations. Results show an average success rate of 87 %, a 2.4x reduction in latency relative to cloud baselines, and strong privacy preservation through zero-knowledge proofs. User studies show 27 % higher trust scores when decision trails are available. These findings establish a foundation for trustworthy autonomous agents in privacy-sensitive financial domains.