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gjm comments on Open thread, June 20 - June 26, 2016 - Less Wrong Discussion
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Yup. The most sophisticated approach I've seen, which is clearly not actually sophisticated enough, is to guess at possible trajectories of future investment growth by some process along the lines of random sampling of past stock market returns, and then choose a sum that leads to you not running out of money in, say, at least 99% of those trajectories.
It's a better start than simple compounding interest calculations :-)
To approach this from another side, one can buy an annuity (which provides a stream of income for the rest of your life). You need to save as much as is needed to buy such an annuity and then you're good (mostly). However I understand that these annuities are not... attractively priced, especially if you want one which adjusts your income stream for inflation.
That is also my understanding, and I doubt the annuity market has the properties required to make its prices reflect any sort of reality.