In this paper, first, we study mean-absolute deviation (MAD) portfolio optimization model with cardinality constraints, short selling, and risk-neutral interest rate. Then, in order to insure the investment against unfavorable outcomes, an extension of MAD model that includes options is considered. Moreover, since the data in financial models usually involve uncertainties, we apply robust optimization to the MAD model with options. Finally, a data set of S&P index is used to compare the effectiveness of options in the models in terms of returns and Sharpe ratios.

中文翻译：

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附加约束下带或不带期权的投资组合优化模型

在本文中，首先，我们研究具有基数约束，卖空和风险中性利率的平均绝对偏差（MAD）投资组合优化模型。然后，为了确保投资免受不利结果的影响，考虑了包括期权在内的MAD模型的扩展。此外，由于财务模型中的数据通常涉及不确定性，因此我们对带有选项的MAD模型进行了稳健的优化。最后，使用标准普尔指数的数据集来比较模型中期权的收益率和夏普比率。