EDA with Switching Distributions for Long-Short Portfolio Replication Problems

It is desired to replicate the benchmark portfolio when it has delivered good performances. In this paper, our focus is on the portfolio replication problem that the total return of the benchmark portfolio is opened to the public but the proportion-weighted combination is closed to the public. It is difficult to solve this replication problem because we cannot have any techniques to solve the simultaneous equations when the number of unknown valuables is more than the number of equations. In order to solve such a problem, we propose the new Estimation of Distribution Algorithm with the operation switching two distributions in this paper. In the numerical experiments, we show that the portfolios replicated by our proposing algorithm have delivered good performances even in the future periods.