Bet A high on the river

[Peter-23]

Say you have AK in the big blind.
A couple of players limp, you raise.
You miss the flop but its not too scarry so you bet anyway.
You get one caller and are out of position for the rest of the hand.

The caller is semi-loose and you cant really put him on a hand. He could be on a draw or he could have hit a pair.

The turn is a blank, you bet trying to steal the pot, he calls.

The river is blank.

What do you do? Do you make the final bet with A high? Do you check/fold, check/call or what?