Portfolio Optimization under Double Heston Duffie-Kan Model and the Price Calculation of the European Option

In this paper, we present a new version of the Double Heston model, where the mixed Duffie-Kan model is used to predict the volatility of the model instead of the CIR process. According to this model, we predict the stock price and calculate the European option price by using the Monte-Carlo method. Finally, by applying the proposed model, we find the optimal portfolio under the Cardinality Constraints Mean–Variance (CCMV)  model and compare it with the mixed Double Houston model and show its efficiency.