Before revision: It has been understood that the `` local" existence of the Markowitz' optimal portfolio or the solution to the local risk minimization problem is guaranteed by some specific mathematical structures on the underlying assets price processes (called ``Structure Conditions" in the literature ){\it   .
After revision: It has been understood that the `` local" existence of the Markowitz' optimal portfolio or the solution to the local risk minimization problem is guaranteed by some specific mathematical structures on the underlying assets price processes known in the literature ){\it .