In this paper, we formulate methods for portfolio selection for investors with different attitudes in the return-risk trade-off. We defined an objective function based on the Sharpe ratio (Sharpe 1966) and downside risk (Fishburn 1977), plus introducing two new terms called "upside volatility" and "diversification". We propose the maximization of the objective function w.r.t. the portfolio weights as a method of determining suitable weights. We also propose practical methods for controlling the expected return while minimizing risk, or controlling risk while maximizing expected return. Experiments showed that the proposed methods yielded successful results.
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