This is more a theoretical problem rather than a technical one.
I am looking for a clear and rigorous definition of corner portfolios and I like to understand more precisely their relation with the mean-variance/minimum variance frontier.
I noticed divergent views while reading about this topic and the related two-funds theorem (i.e. this question).
Does the two-funds theorem apply to the entire minimum-variance frontier or just to the efficient frontier? In other words both frontiers can be derived with a linear combination of portfolios suitably chosen?
Is it correct asserting that deriving the efficient frontier by recurring to the two-funds theorem requires the use of two efficient portfolios that are also corner portfolios for the linear combination?
Is it correct that the two-funds separation theorem is valid only when there is no corner portfolio between the two used in the linear combination at least when deriving the efficient frontier? (Efficient Asset Management by Michaud)
Unfortunately, in some books and papers "mean-variance optimal" and "mean-variance efficient" are used interchangeably.