It is very standard in economics, game theory, etc, to model risk aversion as a concave utility function. If you want some motivation for why, then e.g. the Von Neumann–Morgenstern utility theorem shows that a suitably idealized agent will maximize utility. But in general, the proof is in the pudding: the theory works in many practical cases.
Of course, if you want to study exactly how humans make decisions, then at some point this will break down. E.g. the decision process predicted by Prospect Theory is different from maximizing utility. So in general, the exact flavour of risk averseness exhibited by humans seems different from what Neumann-Morgenstern would predict.
But at that point, you have to start thinking whether the theory is wrong, or the humans are. :)
But in general, the proof is in the pudding: the theory works in many practical cases.
Show me. We are talking about real life (“works”, “practical”), right?
Note that in finance where miscalculating risk can be a really expensive mistake that you pay for with real money, no one treats risk as a trivial consequence of a concave utility function.
But at that point, you have to start thinking whether the theory is wrong, or the humans are.
You might. It should take you about half a second to decide that the theory is wrong. If it takes you longer, you need to fix your thinking :-P
I’m not sure what you have in mind for treatment of risk in finance. People will be concerned about risk in the sense that they compute a probablility distribution of the possible future outcomes of their portfolio, and try to optimize it to limit possible losses. Some institutional actors, like banks, have to compute a “value at risk” measure (the loss of value in the portfolio in the bottom 5th percentile), and have to put up a collateral based on that.
But those are all things that happen before a utility computation, they are all consistent with valuing a portfolio based on the average of some utiity function of its monetary value. Finance textbooks do not talk much about this, they just assume that investors have some preference about expected returns and variance in returns.
It is very standard in economics, game theory, etc, to model risk aversion as a concave utility function. If you want some motivation for why, then e.g. the Von Neumann–Morgenstern utility theorem shows that a suitably idealized agent will maximize utility. But in general, the proof is in the pudding: the theory works in many practical cases.
Of course, if you want to study exactly how humans make decisions, then at some point this will break down. E.g. the decision process predicted by Prospect Theory is different from maximizing utility. So in general, the exact flavour of risk averseness exhibited by humans seems different from what Neumann-Morgenstern would predict.
But at that point, you have to start thinking whether the theory is wrong, or the humans are. :)
Show me. We are talking about real life (“works”, “practical”), right?
Note that in finance where miscalculating risk can be a really expensive mistake that you pay for with real money, no one treats risk as a trivial consequence of a concave utility function.
You might. It should take you about half a second to decide that the theory is wrong. If it takes you longer, you need to fix your thinking :-P
I’m not sure what you have in mind for treatment of risk in finance. People will be concerned about risk in the sense that they compute a probablility distribution of the possible future outcomes of their portfolio, and try to optimize it to limit possible losses. Some institutional actors, like banks, have to compute a “value at risk” measure (the loss of value in the portfolio in the bottom 5th percentile), and have to put up a collateral based on that.
But those are all things that happen before a utility computation, they are all consistent with valuing a portfolio based on the average of some utiity function of its monetary value. Finance textbooks do not talk much about this, they just assume that investors have some preference about expected returns and variance in returns.