Is an armed ship owned by private persons and holding a government commission to attack and capture?

Corsairs were the pirates in mostly the 16th to 18th century, holding a king's commission to attack and rob ships. They were private persons (several famous later admirals started out as corsairs) but their commission only covered ships of a country that their king was at war with. If they were in turn caught by the enemy, they were on their own. If they were succesful they could use their counties' harbors as safe havens and were expected to pay part of their loot or its proceeds into the country's or the King's coffers.