In financial engineering, portfolio optimization has been of consistent interest. Portfolio optimization is a process of modulating asset distributions to maximize expected returns and minimize risks. To obtain the expected returns, deep learning models have been explored in recent years. However, due to the deterministic nature of the models, it is difficult to consider the risk of portfolios because conventional deep learning models do not know how reliable their predictions can be. To address this limitation, this paper proposes a probabilistic model, namely predictive auxiliary classifier generative adversarial networks (PredACGAN). The proposed PredACGAN utilizes the characteristic of the ACGAN framework in which the output of the generator forms a distribution. While ACGAN has not been employed for predictive models and is generally utilized for image sample generation, this paper proposes a method to use the ACGAN structure for a probabilistic and predictive model. Additionally, an algorithm to use the risk measurement obtained by PredACGAN is proposed. In the algorithm, the assets that are predicted to be at high risk are eliminated from the investment universe at the rebalancing moment. Therefore, PredACGAN considers both return and risk to optimize portfolios. The proposed algorithm and PredACGAN have been evaluated with daily close price data of S&P 500 from 1990 to 2020. Experimental scenarios are assumed to rebalance the portfolios monthly according to predictions and risk measures with PredACGAN. As a result, a portfolio using PredACGAN exhibits 9.123% yearly returns and a Sharpe ratio of 1.054, while a portfolio without considering risk measures shows 1.024% yearly returns and a Sharpe ratio of 0.236 in the same scenario. Also, the maximum drawdown of the proposed portfolio is lower than the portfolio without PredACGAN.

翻译：在金融工程领域，投资组合优化一直是持续关注的热点。投资组合优化是通过调整资产配置以最大化预期收益并最小化风险的过程。为获取预期收益，近年来深度学习模型得到了广泛探索。然而，由于这些模型具有确定性特征，传统深度学习模型难以考量投资组合的风险，因为它们无法评估自身预测的可靠性。针对这一局限，本文提出了一个概率模型——预测辅助分类器生成对抗网络（PredACGAN）。所提出的PredACGAN利用了ACGAN框架的特性，即生成器的输出构成一个概率分布。尽管ACGAN此前尚未被用于预测模型，通常仅用于图像样本生成，但本文提出了一种将ACGAN结构应用于概率预测模型的方法。在此基础上，进一步提出了利用PredACGAN获取风险度量的算法。该算法在投资组合再平衡时刻，将预期高风险资产从投资范围内剔除。因此，PredACGAN通过同时考量收益与风险来优化投资组合。本文使用1990年至2020年标普500指数日收盘价数据对所提算法与PredACGAN进行了评估。实验场景设定为根据PredACGAN的预测与风险度量每月进行投资组合再平衡。结果表明，采用PredACGAN的投资组合年化收益率为9.123%，夏普比率为1.054；而在相同场景下，未考虑风险度量的投资组合年化收益率为1.024%，夏普比率为0.236。此外，本文所提投资组合的最大回撤低于未使用PredACGAN的投资组合。