Linear Optimization in C (Ω) and Portfolio Insurance

Abstract

Suppose that X is a subspace of C ( z ) generated by n linearly independent positive elements of C ( z ). In this article we study the problem of minimization of a positive linear functional p of X in X , under a finite number of linear inequalities. This problem does not have always a solution and if a solution exists we cannot determine it. In this article we show that if X is contained in a finite dimensional minimal lattice-subspace Y of C ( z ) (or equivalently, if X is contained in a finite dimensional minimal subspace Y of C ( z ) with a positive basis) and m = dim Y , then the minimization problem has a solution and we determine the solutions by solving an equivalent linear programming problem in . Finally note that this minimization problem has an important application in the portfolio insurance which was the motivation for the preparation of this article.

Keywords:

• Linear Optimization
• Lattice Subspace
• Projection Basis
• Portfolio Insurance