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Mean-variance is the starting point of most portfolio optimisation techniques.

Mean-variance is the starting point of most portfolio optimisation techniques: one usually want to maximise the expected returns (i.e. the mean of the future returns of the portfolio), while minimising the risk (i.e. the variance) taken to maintain the associated exposure.

It started with Markowitz paper assuming market participants are all using a mean-variance preference function, and reasoning in terms of representative agent, implied the average expected returns anticipated by asset managers. Cf. Markowitz, Harry. "Modern portfolio theory." Journal of Finance 7, no. 11 (1952): 77-91.

In Modern Portfolio Theory (that is the continuation and extension of Markowitz ideas), the future is i.i.d.

Then Merton formulated the problem adding time in the picture, cf. Merton, Robert C. "Lifetime portfolio selection under uncertainty: The continuous-time case." The review of Economics and Statistics (1969): 247-257.