Computational methods in lattice-subspaces of C[a,b] with applications in portfolio insurance

In this article, we develop a computational method for an algorithmic process first posed by Polyrakis in 1996 in order to check whether a finite collection of linearly independent positive functions in C[a,b] forms a lattice-subspace. Lattice-subspaces are closely related to a cost minimization problem in the theory of finance that ensures the minimum-cost insured portfolio and this connection is further investigated here. Finally, we propose a computational method in order to solve the minimization problem and to calculate the minimum-cost insured portfolio. All of the numerical work is performed using the Matlab high-level language.