Optimal allocation algorithm of financial re-sources based on return-risk equilibrium

To effectively balance the relationship between financial resource allocation, returns, and risks, a financial resource op-timization allocation method based on the Bayesian filtering algorithm is proposed. This method combines prior infor-mation and observed data to predict and update financial market risks through Bayesian filtering, thereby establishing a profit-risk balanced financial resource optimization allocation model. Utilizing fuzzy set theory, the multi-objective op-timization problem is transformed into a single-objective optimization problem, specifically maximizing the return-risk index. By employing an improved particle swarm optimization algorithm, the optimal allocation of financial resources and input ratios are determined. The research results demonstrate that within a risk division range of $ 3*10^{-5} $, this meth-od achieves maximized returns, effectively balancing returns and risks in financial resource allocation, validating its practicality and effectiveness.