MAPLE code for the gamma algorithm for global optimization of uncertain functions in economy and finance

Abstract

Problems with uncertainties are ubiquitous in many areas of life and the economy. Due to a lack of information as regards the economy and in finance, problems with uncertainties (stock prices, marketing problems, inflation, unemployment) are usually formulated by giving bounds on maximum and minimum values of certain parameters, i.e. box constraints. In such situations, it is necessary to make a choice of better parameters that produce finite intervals of possible values for a given uncertain function at each point of the parameter space. The gamma algorithm presents a method for making that choice. A variant of the gamma algorithm based on the cubic algorithm is considered, for global optimization of uncertain functions with box constraints in Rn. The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]n for all problems. On this basis, a MAPLE code of modular structure is developed for full global optimization of uncertain functions in n variables. The code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. An example related to Minsky’s Financial Instability Hypothesis is presented, with a graph, to illustrate the use of the code.