Okay, here's what we have so far:

If portfolio returns are lognormally distributed with Mean and Standard Deviation M and S, and g1, g2, g3 ... are annual gain factors and I = 1 + i = 1 + InflationRate is the annual inflation factor and M = I e-(M - S2/2) and S2 = I2e-2(M-S2/2)[eS2-1] = M2[eS2-1] then a $1.00 portfolio, after n years, is worth:   g1g2...gn[1 - WgMS(n)] where W is the (initial) withdrawal rate (increasing with inflation) and gMS(n) = I/g1 + I2/g1g2 + I3/g1g2g3 + ... + In/g1g2...gn Note that Mk and Sk are the Mean and Standard Deviation of a typical term in gMS, namely Ik/g1g2...gk. In order that your portfolio survive n years:   gMS(n) < 1/W. Further we have: Mean(gMS(n)) = M (1 - Mn) / (1 - M) SD(gMS(n)) = {2/LOG(A)} {SQRT[An-1] - ARCTAN[SQRT[An-1]]} where A = 1 + S2/M2

... don't trust nothin' ... yet