5 ms·

Sigh, "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 effec

Sigh, "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 ago
  No 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 ago
    Could 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.
    - deleted 6y ago
      [deleted]
    - kgwgk 6y ago
      I 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 ago
        His 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...
        ReflectedImage 6y ago
        I'm sure there are some great research papers that can be written by applying ergonomic economics to those problems. Is your point here that Ole Peters should convert all problems in economics to ergonomics economics all at once? Cause that's a bit of a silly point to make. There is also a fundamental problem with expected utility theory in that U can set to any formula. It's pretty close to just making stuff up on the fly.
        6y ago
throwaway98797 6y ago
Kelly 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 ago
  I 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 ago
  You 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.”

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 ago
No 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 ago
  Could 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.
  - deleted 6y ago
    [deleted]
  - kgwgk 6y ago
    I 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 ago
      His 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...
        ReflectedImage 6y ago
        I'm sure there are some great research papers that can be written by applying ergonomic economics to those problems. Is your point here that Ole Peters should convert all problems in economics to ergonomics economics all at once? Cause that's a bit of a silly point to make. There is also a fundamental problem with expected utility theory in that U can set to any formula. It's pretty close to just making stuff up on the fly.
        6y ago

throwaway98797 6y ago

Kelly 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 ago
I 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 ago
You 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.”