Production method for olefin-based polymer, olefin polymerization catalyst, and olefin-based polymer

In this production method for an olefin-based polymer, an olefin is polymerized using a transition metal compound (A), a boron compound (B) which forms an ion pair with component (A), an organoaluminium compound (C), and water (D). The molar ratio [(D)/(A)] of the molar amount of component (D) to the molar amount of the transition metal in component (A) is at least 5, but not more than 10000.