C. Asinius Pollio (76 BC-AD 4): see generally OCD(4) 184. He fought with Julius Caesar in his campaigns of the Civil War and later supported Mark Antony. He retired from politics before the showdown with Octavian/Augustus to devote himself to literature. A friend of Catullus, Horace and Vergil, he was best known for his lost Histories covering the origins of the Civil War and its course down at least to the death of Cicero (for whom he had profound contempt throughout his life), and probably the battle of Philippi. If he covered Greek history it can only have been incidental to the campaigns fought in Greece.
See also pi 2165, where, however, this man seems to be conflated with Asinius Pollio of Tralles; cf. G.W. Bowersock, Augustus and the Greek World (Oxford 1965) 110 with n.5.