<p>We provide a rigorous mathematical approach to the beta-pricing model, starting from the classical two-step cross-sectional regression, through Nonlinear Seemingly Unrelated Regression (NSUR) and Generalised Methods of Moments (GMM), and finally compare the results with several linear approximation methods. The use of the linear approximation applied to a system of nonlinear equations is new in the literature and is the major contribution of this article, together with a linear-programming L1-norm estimator that is more robust than classical alternatives under heavy-tailed errors. Many real-world problems involve nonlinear product terms of variables, for which linear approximation simplifies analysis, enhances computational efficiency, and allows for the application of standard linear programming. We explore three main methods with several variants used with linear approximation for product functions, including Taylor approximations, McCormick relaxation, and piecewise linear functions with Mixed-Integer Linear Programming (MILP). Our results show that, in the presence of heavy-tailed distributions, the L1-norm methods proposed in this study are more appropriate (exhibiting lower bias and variance) for risk premium estimation than traditional L2-norm approaches. Financial returns are often heavy-tailed and non-Gaussian. L1-based estimation offers robustness to such features and motivates our linearization approach.</p>