This utility function has near zero risk aversion at relevant range.

Assuming our AI has wealth level of $10000, it will happily take a 50:50 bet of gaining $100.10 vs losing $100.00.

Yes, it is weak risk aversion - but is it not still risk aversion, as I had initially meant (and initially thought you to mean)?

It also gets to infinities if there's a risk of dollar worth below -$10.

Yes, of course. I'd considered this irrelevant for reasons I can't quite recall, but it is trivially fixed; is there a problem with U(x) = x/log(x+10)?