Optimal portfolio selection and compression in an incomplete market

We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modelled as diffusions and the market is incomplete. We find an explicit solution for the case of limited diversification of the portfolio, i.e. for the portfolio compression problem. By this we mean that any admissible strategy may include no more than m different stocks concurrently, where m may be less than the total number n of available stocks.