No free lunches & MPT
I could enunciate it, but wikipedia has an explanation. I honestly don't understand the Wikipedia explanation, but I would expect that it explains my intuitions in a more technical way than I do. If you have a specific point of disagreement, I'm happy to map out my logic and explore the evidence with you. I vaguely remember reading an article on the topic, too.
Optimal bet sizing and expected utility
I'd expect a theorem to maximise utility via diversification would entail some prediction that the utility of subsequent/other/more investments will be greater than the utility of the first/reference investment. If that isn't the case, it will lower the average expected utility of one's portfolio. I don't see the rationale behind the Kelly criterion as it related to any of my existing knowledge about maximising utility.
MPT: How can I have a specific point of disagreement with something as nonspecific as "I am not convinced by modern portfolio theory because no free lunches"? The particular but of the Wikipedia article you linked to actually says (correctly, so far as I can see) that minimising unsystematic risk through diversification (as indicated by MPT) is "one of the few free lunches available" because unsystematic risk isn't associated with higher expected returns.
Kelley: Actually most of the paragraph ostensibly about this seems to be still abou...
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