Abstract
It is desired to make the replication portfolio when a benchmark portfolio has delivered good returns. However, the portfolio replication problem is one of equality constrained indeterminate problems. We cannot find the same proportion-weighted combination as the benchmark portfolio by minimizing the evaluation values of solutions even if we use any evolutionary algorithm. We have an important problem that minimizing the evaluation value does not depend on improving the solution. In order to solve this problem, we propose a new model which removes the equality constraint in the optimization problem in this paper. Our model transforms the equality constrained search space to the unconstrained search space for the portfolio replication problems. In the numerical experiments, we show that the evolutionary algorithms can generate the good solutions by minimizing the evaluation values in the unconstrained search space obtained by our model.
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