Portfolio Optimization under Fractional and Uncertain Processes: A Comparative Approach using Mixed Brownian and Liu Models

In the face of increasingly volatile and ambiguous financial markets, traditional portfolio optimization models often fall short in capturing long-memory dependencies and human behavioral uncertainties. This study proposes an advanced comparative framework that integrates mixed fractional Brownian motion and Liu's uncertainty theory to optimize investment portfolios. Three modeling approaches are examined: classical Brownian motion, mixed fractional Brownian motion, and uncertain differential equations. By implementing both mean-variance and mean-absolute deviation optimization techniques, we evaluate the performance and robustness of portfolios across these stochastic and uncertain environments. Numerical experiments based on real financial data demonstrate that models incorporating fractional or uncertain processes achieve better risk-adjusted returns and exhibit greater stability under extreme market conditions. The results highlight the potential of hybrid modeling frameworks to more accurately reflect market realities and improve decision-making in portfolio management. This research provides valuable insights for financial analysts, quantitative researchers, and decision-makers seeking to enhance portfolio performance under uncertainty and memory effects.

کلیدواژه ها:

Portfolio Optimization ، Fractional Brownian Motion ، Uncertainty Theory ، Mixed Stochastic Processes ، Liu Process ، Mean-Variance Model ، Risk Management ، Financial Modeling