Utilizing RNN based model and bi-objective programming to a new mean-conditional value at risk-entropy for uncertain portfolio optimization with liquidity and diversification

This paper addresses a portfolio optimization problem characterized by uncertain returns. In this context, the returns of risky assets are viewed as uncertain variables, estimated by experienced experts. Initially, a mean-Conditional Value at Risk-entropy model is proposed for the uncertain portfolio optimization problem, considering four criteria: return, risk, liquidity, and the diversification degree of the portfolio. In this model, investment return is determined by the uncertain expected value, investment risk is represented by uncertain Conditional Value at Risk, and entropy is used to measure the diversification degree of the portfolio. Furthermore, our model differs from previous bi-objective optimization models by integrating both maximum return and minimum risk into a single objective form through the introduction of a risk aversion factor and the removal of dimensional influences caused by different units via a normalization method. Subsequently, several auxiliary portfolio selection models are converted into different equivalent deterministic models. Utilizing a neural network strategy with reducing dimension and complexity, the resulting single-objective optimization problem is solved. Based on Lyapunov theory, the proposed model is proven to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the achieved mathematical programming problem for different weight values. The efficient frontier (Pareto Optimal Solution) is also provided using different weight values. Additionally, these algorithms determine an approximation of the set of efficient elements and diversify the solutions along the Pareto front. Computer simulations demonstrate the effectiveness and practicality of the proposed model.