An Algorithm for Determining the Controllers of Supervised Entities at the First and Second Levels: A Case Study with the Brazilian Central Bank

Abstract

An algorithm was developed and implemented to find controllers from the stock shares for some financial institutions for the Brazilian Central Bank (BCB). The original problem is similar to a typical Sum of Subset problem that is suggested to be solved by a backtracking algorithm and the problem complexity is NP-complete. Usually BCB solves this problem manually which is time consuming and prone to errors. The heuristical approximation algorithm presented in this paper has polynomial complexity O(n3) and is based on sub-routines for determining controllers at the first two levels. The paper describes the basic concepts and business rules currently employed in BCB, our algorithm and its major subroutines, it gives a brief complexity analysis and an example illustration at level 2. Our experimental results indicate the feasibility of an automation of the process of finding controllers. Though developed for BCB, our algorithm works equally well for other financial institutions.