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And what result is that? Most of this is well-known. Ergodicity is a concept that's covered in econometrics classes. "When are time averages the averages of

And what result is that? Most of this is well-known. Ergodicity is a concept that's covered in econometrics classes. "When are time averages the averages of the underlying probability distribution?" is the first topic in time series. Honestly, the whole approach is a step back. People discussed these ideas back when Kelly first published the Kelly rule, and the conclusion is that most people are not that aggressive in their investment decisions. People still study it, though, (it's called the growth optimal portfolio), and its properties are well-known. Peters also sneaks in a second assumption, which is that the growth rate of wealth is ergodic. Is it? That's not clear to me at all.

ReflectedImage 6y ago
"most people are not that aggressive in their investment decisions" That's because Kelly's criterion is a special case of Ole Peters, where Kelly's is a very aggressive option. There are other criterion that can be used, which are not so aggressive. Ole Peters lists the class of functions that can be used in his paper. So basically economics has rejected it for the wrong reason.
- QuesnayJr 6y ago
  As far as I can tell, he lists wealth, and log wealth as the two possible criteria. If there are others, I missed them. If you try to match a power utility model with stock market data, to match prices on the stock market, you would reject both the additive model (eta = 0) and the multiplicative model (eta = 1), in favor of an eta greater than 10. This is known as the equity premium puzzle. The thrust of research over the past 30 years in explaining stock prices has been to reject both Peters' models, and expected utility in general. People build their entire careers on investigating alternatives. There are hundreds of experiments to explain, plus all of the real-world data. It turns out that explaining all of this with one unified model is hard.
  - ReflectedImage 6y ago
    Those are the EUT criteria not Ole Peters. The maths you are looking for is here: https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf https://ergodicityeconomics.files.wordpress.com/2018/06/ergo...

ReflectedImage 6y ago

"most people are not that aggressive in their investment decisions" That's because Kelly's criterion is a special case of Ole Peters, where Kelly's is a very aggressive option. There are other criterion that can be used, which are not so aggressive. Ole Peters lists the class of functions that can be used in his paper. So basically economics has rejected it for the wrong reason.

QuesnayJr 6y ago
As far as I can tell, he lists wealth, and log wealth as the two possible criteria. If there are others, I missed them. If you try to match a power utility model with stock market data, to match prices on the stock market, you would reject both the additive model (eta = 0) and the multiplicative model (eta = 1), in favor of an eta greater than 10. This is known as the equity premium puzzle. The thrust of research over the past 30 years in explaining stock prices has been to reject both Peters' models, and expected utility in general. People build their entire careers on investigating alternatives. There are hundreds of experiments to explain, plus all of the real-world data. It turns out that explaining all of this with one unified model is hard.
- ReflectedImage 6y ago
  Those are the EUT criteria not Ole Peters. The maths you are looking for is here: https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf https://ergodicityeconomics.files.wordpress.com/2018/06/ergo...