This paper proposes a multiobjective portfolio selection problem with most probable random distribution derived from current market data and other random distributions of boom and recession under the risk-controlled parameters determined by an investor. The current market data and information include not only historical data but also interpretations of economists' oral and linguistic information, and hence, the boom and recession are often caused by these nonnumeric data. Therefore, investors need to consider several situations from most probable condition to boom and recession and to avoid the risk less than the target return in each situation. Furthermore, it is generally difficult to set random distributions of these cases exactly. Therefore, a robust-based approach for portfolio selection problems using the only mean values and variances of securities is proposed as a multiobjective programming problem. In addition, an exact algorithm is developed to obtain an explicit optimal portfolio using a principle of compromise.
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