Suppose you want to maximize your long run growth rate. You sample from a normal distribution with finite mean and variance(m,v), let us call that sampled value x.
You can either resample another random x, or grow by 8%(x(1+0.08) for sure, and this can always be done. So if you get a low number, you can just resample.
It seems obvious that the optimal strategy will be to have some threshold, t, where if the value of x is greater than this threshold then you go with the deterministic growth otherwise you resample.
Now the question is: is there a closed form for this t? Initially, I thought the variance ought not to play a role but upon further reflection, I think it must, there should be a parallel to pricing of financial options.