growth optimal strategy

One of the motivations of minimizing variance is that the estimate of geometric mean as mu - sigma^2 is closer than just mu in approximating the geometric mean of return. geometric mean of the returns (in case all the wealth is bet in every round) is the growth rate. To summarize, the growth rate is g such that ln(1+g) = {Prod(i in 1:T)[1 + b Ri]} / T .
Hence approximating ln(1 + g) as g, maximizng growth rate amounts to maximizing return.