Amplitudes in the quantum-mechanical superposition of the multiverse, that is. Getting philosophy-of-probability issues straight, and then deciding they are less important than issues of psychology...
the premise of most American movies over the last 120yrs - from buster Keaton to James Stewart to Bruce Willis to Kano Reeves - is that our guy is improbably lucky. it's our national church sermon. when it's a 1 and 100 chance and our guy *doesn't* make it, it's a tragedy, not just fucking normal.
I think you have overlooked the strongest reason of all why trading firms bet according to the Kelly criterion. Trading firms do not in fact believe that they live in an ensemble of stochastic trajectories ("the multiverse") and that their job is to maximize the expectation of wealth over all these trajectories at some time. They believe that they live in a single stochastic trajectory and that their job is to maximize the expected growth of wealth pathwise, on this single trajectory indefinitely. Another way of saying this is that they are interested in almost sure convergence, not just convergence in probability.
the premise of most American movies over the last 120yrs - from buster Keaton to James Stewart to Bruce Willis to Kano Reeves - is that our guy is improbably lucky. it's our national church sermon. when it's a 1 and 100 chance and our guy *doesn't* make it, it's a tragedy, not just fucking normal.
I think you have overlooked the strongest reason of all why trading firms bet according to the Kelly criterion. Trading firms do not in fact believe that they live in an ensemble of stochastic trajectories ("the multiverse") and that their job is to maximize the expectation of wealth over all these trajectories at some time. They believe that they live in a single stochastic trajectory and that their job is to maximize the expected growth of wealth pathwise, on this single trajectory indefinitely. Another way of saying this is that they are interested in almost sure convergence, not just convergence in probability.
Yes...
Excellent. I'm figuring out how to write about B-F right now. Mania is looking good to me at the moment.
Yes...