The standard way to model risk aversion mathematically is to have DMU from additional amounts of money (or wealth). For example, if your utility from wealth is U = SQRT(W), then you would be risk averse. Note that you would get more utility from a certain $1000 in wealth, rather than a 50% chance of $500 and a 50% chance of $1500, if we assume you act to maximize the expectation of utility.
If you want to see more on this, the Wikipedia article is a good place to start:
https://en.wikipedia.org/wiki/Expected_utility_hypothesis#Risk_aversion
