I'm looking at a download of BlackRock's capital market assumptions, which gives a bunch of statistics, such as expected and quartiles for asset classes' returns for different timeframes, volatilities and very partial correlations. (But no correlation matrix for example, nor any other specifications of distributions.)
I would like to create a set of - say - 100,000 histories, that together fit those statistics.
I'm thinking of starting with one random history, and then keep adding random histories that increase the 'overall fit' of the collection of histories (if not, then do not add this particular history and move to the next).
But I have the feeling that I am reinventing something that already exists. Is a technique like the above well-known (or is there a well-known better one)?