= Discrete geometric average under the stock-numeraire measure
{title2=$\log A\sim N(m,v)$}
For sampling times $t_i$ and $\bar t=n^{-1}\sum_it_i$, the <geometric mean> $A=(\prod_i S_{t_i})^{1/n}$ has $\log A$ normally distributed under the <stock-numeraire measure in the Black-Scholes model>. Its mean is $\log S_0+(\rho+\sigma^2/2)\bar t$, and its <variance> is $v=\sigma^2n^{-2}\sum_{i,j}\min(t_i,t_j)$. For descending times the sum is $\sum_i(2i-1)t_i$. The drift shift comes from exponential tilting, and must be included when the delivered payment contains a factor $S_T$.
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