Here's fundamental impossibility result for modeling risk aversion in expected utility framework, and this is for the ridiculously oversimplified and horribly wrong version of "risk aversion" invented specifically for expected utility framework.

Actual risk aversion looks nothing like a concave utility curve, you can get one bet right, then when you change bet size, bet probability, wealth level or anything, you start getting zeroes or infinities where you shouldn't, always.

Prospect theory provides simple models that don't immediately collapse and are of some use.