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As a stats PhD, I am telling you Ole Peters is misunderstanding what EUT is ;-) EUT was developed by von Neumann, someone slightly familiar with ergodicity. It
by zwaps 6y ago
As a stats PhD, I am telling you Ole Peters is misunderstanding what EUT is ;-)
EUT was developed by von Neumann, someone slightly familiar with ergodicity. It simply is not based on dynamics of out-of-equilibrium systems. Any such thing is an application that adds assumptions to the construct.
Ergodicity is an obvious addition in the time domain, it is so obvious that the insight is not even new. However, Peters restricts the problem to a very simple dynamic gamble and then claims that all of economics must be wrong.
The very first sentences of Peter's article already get this completely wrong.
If you insist on his results, despite the quoted article, the most one can say is that the application of EUT to these problems is questionable.
To put it in terms you may be more familiar with. It's like saying that Object Oriented Programming is "wrong", because Python doesn't work for my problem at hand.
- ReflectedImage 6y agoSigh, "Ergodicity is an obvious addition in the time domain" Great, except Ole Peters if you understood his work is adding non-ergodicity. Ole Peters is effectively claiming that static gambles don't exist (outside of utterly bizarre circumstances like parallel universes or co-operatives). The set of problems that you can use EUT on and be correct is almost zero. To simplify: You must always use the Kelly's criteria even for single one-off gambles otherwise you have got the wrong answer. (There are other valid criteria then Kelly's that you could also use but you need to read Ole Peters' paper for them)
- kgwgk 6y ago> The set of problems that you can use EUT on and be correct is almost zero. But his theory is applicable in a strict subset of those...
- ReflectedImage 6y agoNo his theory is applicable to a much wider domain. Basically 99.5% of problems that are being solved with EUT should be solved with ergodicity economics. EUT validity is crushed down to the 0.5%.
- kgwgk 6y agoCould you point to one example where a problem is solved and their solution is not equivalent to the choice of an utility function?
- ReflectedImage 6y ago@kgwgk Ahh misread for a second there. Prospect theory is a good example. When calculated using Ole Peters method Prospect theory does not exist.
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- kgwgk 6y agoI don't understand what you mean. Prospect theory tries to solve the problems with EUT. His methods are within the EUT framework. Whatever the problems in EUT that are solved by prospect theory, they also need to be solved in his theory.
- ReflectedImage 6y agoHis methods are a replacement to the EUT framework. When you attempt to do Prospect theory with Ergonomic Economics you get back the null result: "People behave as rational actors" Rather than the EUT's result of: "Faced with a risky choice leading to gains, individuals are risk-averse (concave value function). Faced with a risky choice leading to losses, individuals are risk-seeking(convex value function)." Basically ergonomics economics shows that Prospect theory is a math's error. This is one of the reasons why Ole Peters work is important.
- kgwgk 6y ago> His methods are a replacement to the EUT framework. What's the solution to this problem using his methods, for example? https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem How do his methods apply to the uncountable situations where expected utility theory is used? A random example: https://www.researchgate.net/publication/240488954_Risk_of_dam_failure_in_benefit-cost_analysis https://www.researchgate.net/publication/240488954_Risk_of_d...
- throwaway98797 6y agoKelly maximizes the median outcome, I think. I’ve yet to find an approach that minimize the bottom x percentile. If you’re aware of one I’d love to learn it.
- hntrader 6y agoI think you mean something that maximizes the bottom x percentile (either by making the negative smaller or the positive bigger). It's not going to be an easy solution, because for a sufficiently small x, the optimal strategy for a small number of bets is going to be to bet $0 each time (since the x-th percentile of the terminal outcome will be a loss on capital, or ruin), but the optimal strategy for a large number of bets is going to be to bet > $0 (since the x-th percentile of the terminal outcome will be positive). So we can already see that this is going to be a function of the number of bets, unlike with Kelly, and therefore is going to be a much harder problem.
- kgwgk 6y agoYou may find this interesting: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=439400 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=439400 “This paper provides an alternative behavioral foundation for an investor's use of power utility in the objective function and its particular risk aversion parameter. The foundation is grounded in an investor's desire to minimize the objective probability that the growth rate of invested wealth will not exceed an investor-selected target growth rate. Large deviations theory is used to show that this is equivalent to using power utility, with an argument that depends on the investor's target, and a risk aversion parameter determined by maximization. As a result, an investor's risk aversion parameter is not independent of the investment opportunity set, contrary to the standard model assumption.”
- ReflectedImage 6y ago"It simply is not based on dynamics of out-of-equilibrium systems" I think that's basically the key point. Ergodicity economics and the real world are both based on dynamic out of equilibrium systems. Where regular economics is not. Real people behave according to ergodicity economics according to Ole Peters study and also the data set used in Prospect's theory.
- rmbeard 6y agoThis is also not correct, it depends on which economic model you are looking at. Some assume equilibrium some study transitory dynamics to the equilibrium. You can't make general statements like that and expect them to be always true, you need to refer to a specific model not the field as a whole.
- ReflectedImage 6y agoIt's true for Expected Utility Theory and anything that has been based on top of it.