DislikedCopernicus, You want robustness in your position sizing with respect to future market conditions. can we stipulate that this is paramount? That being the case (and we are only discussing the simple case of trading one component at a time here), our criterion (in the sizes we are trading in) may not be to maximize (asymptotic) long-term expected growth, but perhaps something else (e.g. maximize MAR ratio, or something like that). We can estimate the peak of the curve as p'/2 because (if you are using the optimal f formula, which is "scaled,"; if...Ignored
I clearly need to look into this more and will refer to your references. I need to mull on this to let it sink in. Quite clearly scaling is something I must do with my modelling which is popping up time and time again.
I have always suspected that I need to delve a bit deeper than expectancy alone with regards to developing a robust system and a few lightbulbs were starting to flicker with your post as the general thrust of what you were saying started to hit home. I unfortunately don't have the requisite skills for intense mathematical modelling so I cheat and ask those incredibly talented mathematicians out there to interpret it for me so I can apply it.
Your contributions to a forum like this will be invaluable and I hope you stick around.
Quidquid latine dictum, altum videtur