P vs NP Problem in Portfolio Optimization: Integrating the Markowitz-CAPM Framework with Cardinality Constraints and Black-Scholes Derivative Pricing
This paper makes the Millennium Prize problem P vs NP operational in quantitative finance by studying cardinality-constrained portfolio selection. Starting from the convex Markowitz mean-variance program with CAPM-based expected returns (Rf plus beta times ERP), we impose a hard sparsity rule that l