[zhdc1]

> Has anyody done a thourough calculation with statistics and all?

Yes. There's a lot of research comparing dollar cost averaging with lump sum investing. Lump sum investing in a diversified portfolio (total market ETF) almost always wins, even in periods where markets are 'overpriced' (e.g., high CAPE 10 ratios).

[funnym0nk3y]

I have heard the same. But how could that be mathematically derived from a stochastic process? AFAIK the stock market is assumed to be a white gaussian process with mean larger than 0. How does the risk of bankrupcy and the variance of the portfoilio value at the end behave? How does it depend on the DCA period?

[jacobr1]

Most mathematical analyses that I've seen involve running prior sequences of real-returns of various lengths though a monte-carlo simulation. So the distributions of prior returns is baked in (via a uniform sampling of historical timeframes).

Here is a good example: https://www.portfoliovisualizer.com/monte-carlo-simulation

Plenty of the white-papers from the big mutual fund firms give the impression they use very similar analysis methods.