Money-pump arguments, on the other hand, can establish this from other assumptions.
Can you say more about this? Stuart’s arguments weren’t that convincing to me, absent other assumptions. In particular, it seems like the existence of a contract that exactly cancels out your own contract could increase the value of your own contract; and that there’s no guarantee that such a contract exists (or can be made without exposing anyone else to risk that they don’t want). Stuart seems to acknowledge this in other parts of the comments, instead referring to the possibility of aggregation.
From this, I’m guessing that you need to assume that the risk is almost independent of the total market value (e.g. because it’s small in comparison with the total market value, and independent of all other sources of risk), and there exists an arbitrarily large number of traders whose utility is linear in small amounts of money (that you can spread out the risk between). Are these the necessary assumptions to establish linearity of utility in money?
Can you say more about this? Stuart’s arguments weren’t that convincing to me, absent other assumptions. In particular, it seems like the existence of a contract that exactly cancels out your own contract could increase the value of your own contract; and that there’s no guarantee that such a contract exists (or can be made without exposing anyone else to risk that they don’t want). Stuart seems to acknowledge this in other parts of the comments, instead referring to the possibility of aggregation.
From this, I’m guessing that you need to assume that the risk is almost independent of the total market value (e.g. because it’s small in comparison with the total market value, and independent of all other sources of risk), and there exists an arbitrarily large number of traders whose utility is linear in small amounts of money (that you can spread out the risk between). Are these the necessary assumptions to establish linearity of utility in money?
I basically think you’re right, those arguments are weak, but this post was about me reasoning out some of the details for myself.
You make a good point about independent risk. I had only half-noticed that point when thinking about this.