Uncertainty-driven portfolio selection via a multi-strategy modified sparrow search algorithm approach

In volatile financial markets, expert estimates play a crucial role when historical data fails to accurately reflect market movements. Meanwhile, investment in financial derivatives is indispensable in the actual financial transaction process. Therefore, this paper delves into an uncertain portfolio selection problem with an exploration of expected utility and options. First, an expected utility-TVaR-entropy model considering loss aversion is established. In this model, the expected utility function depicts wealth changes from portfolio returns, TVaR serves as an accurate risk measurement tool to control risks, and entropy – characterized by its nonlinear nature – is employed to describe diversification, capturing the non-proportional relationships in portfolio diversity. Subsequently, the deterministic forms of the presented models are derived when the stock price follows specific distributions. To solve the model more effectively, a multi-strategy modified sparrow search algorithm is developed, integrating a chaotic mapping strategy, a dynamic boundary strategy, and a hybrid sine cosine algorithm-firefly algorithm search strategy, which is well-suited to handle the nonlinearity introduced by the entropy constraint in the solution space. Finally, the proposed model is numerically simulated, highlighting the advantages of the proposed algorithm. Additionally, the influence of options and loss aversion on the investment strategy is discussed.