Rhodes had the Lex Rhodia (which included a provision granting 'general average'); a sort of group-based insurance scheme for differing ventures to compensate those among the group whose ships were lost. So the concept did indeed exist in (or at least before) Roman times.

The Romans also had life insurance, so the concept of insurance was there.

Genoa most certainly had banking houses issuing insurance and loans -- and their rivals in Venice did as well (but that was more state-oriented and derived). However, I'd agree that there doesn't seem to be much evidence towards institutional insuring in Rome.