In this paper we investigate the problem of speculative processing in a replicated transactional system layered on top of an optimistic atomic broadcast service. We consider a realistic model in which transactions' read/write sets are not known a-priori, and transactions' data access patterns may vary depending on the observed snapshot. We formalize a set of correctness and optimality properties aimed at ensuring that transactions are not activated on inconsistent snapshots, as well as the minimality and completeness of the set of explored serialization orders. Finally, an optimal speculative transaction replication protocol is presented.