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 (called ``Structure Conditions" in the literature ){\it .