Electronic trading (e-trading) provides a virtual marketplace (e-Marketplace) where buyers and sellers can engage in business activities through electronic media rather than direct physical contact. Although negotiation is a fundamental component of e-trading, the critical risks of missing out on top utility offers that expire before client's negotiation deadline has not been addressed. In order to address these problems, we propose a mobile-agent based secure one-to-many bilateral e-trade negotiation framework that efficiently manages the risk of losing top utility offers and maximizes client's utility taking into account various temporal constraints. Theoretical and empirical analysis of the proposed approach is performed. We evaluated the performance of the proposed strategy in terms of client's utility and negotiation time and compared it with two baseline negotiation strategies. The experimental analysis shows that the proposed strategy maximizes client's utility, shortens negotiation time, and ensures adequate market search. Proofs of validity of the proposed utility function are presented. The security protocol is formally verified and the verification shows that the protocol is free of security flaws and hence, negotiation data are secured.