A heuristic process on the existence of positive bases with applications to minimum-cost portfolio insurance in C[a, b]

摘要

In this work we propose an algorithmic process that finds the minimum-cost insured portfolio in the case where the space of marketed securities is a subspace of C[a, b]. This process uses, effectively, the theory of positive bases in Riesz spaces and does not require the presence of linear programming methods. The key for finding the minimum-cost insured portfolio is the existence of a positive basis. Until know, we could check, under a rather complicated procedure, the existence of a positive basis in a prescribed interval [a, b]. In this paper we propose a heuristic method for computing appropriate intervals [a, b], so that the existence of a positive basis is guaranteed. All the proposed algorithmic processes are followed by appropriate Matlab code.