Application of Differential Evolution Algorithms to Portfolio Optimization Problems using Loan

A Study of GP (Genotype-Phenotype) Mapping

Abstract

In this paper, portfolio optimization using loan is formulated as a chance constrained problem in which the money borrowed from a loan is invested in risk assets. Then the chance constrained problem is transformed into a deterministic optimization problem that has an equality constraint. In order to apply conventional Differential Evolution (DE) algorithms to the constrained optimization problem effectively, two types of Genotype-Phenotype (GP) mappings, namely a conventional GP mapping and a newly proposed GP mapping, are compared. As a result of numerical experiments including a two-way analysis of variance (two-way ANOVA), it is shown that the proposed GP mapping outperforms the conventional one because the former enhances the quality of solutions obtained by DE algorithms. By using historical data of assets, an advantage of the investment using loan is also confirmed.