Computation of vector sublattices and minimal lattice-subspaces of ℝK: Applications in finance

In this article we carry out a computational study on Polyrakis algorithms [I.A. Polyrakis, Finite‐dimensional lattice‐subspaces of C(Ω) and curves of ${‐{R}}^n$ , Trans. Am. Math. Soc. 348 (1996) 2793–2810; I.A. Polyrakis, Minimal lattice‐subspaces, Trans. Am. Math. Soc. 351 (1999) 4183–4203]. These algorithms can be utilised for the determination of the vector sublattice and the minimal lattice‐subspace generated by a finite set of positive vectors of ${‐{R}}^k$ . It is demonstrated that the findings of our work can be very useful in the field of Economics, especially in completion by options of security markets and portfolio insurance.