In practice, returns of assets usually do not follow a normal distribution and frequently exhibit heavy tails. Consequently, the normality assumption significantly underestimates risk. It has been suggested that \(\alpha \) -stable distributions are more appropriate for modeling non-normal distributions of returns. Additionally, forecasting asset returns and volatilities are fundamental tasks in both the financial market and portfolio optimization. In this paper, we utilize the \(\alpha \) -stable distributions to capture both the asymmetry and heavy tails of asset returns, while also employing Copula models to examine the dependence structure among returns. To improve the prediction accuracy of the volatilities of assets we examine a integrated model consisting of the traditional econometric model ARMA-GARCH and Stable distribution and a Deep Neural Network, incorporating Copula model, to forecast returns and volatilities of assets in the US stock market. We subsequently apply the proposed integrated model to address Mean-Variance and Conditional Value at Risk (CVaR) optimal portfolio selection problems. Our primary findings indicate that the proposed model outperforms the market index, traditional econometric models, and the integrated model without Copula. We demonstrate that the Student-t Copula performs better in both portfolio optimization problems.
