We propose a new, systematic approach for analyzing and solving heterogeneous-agent models with fat-tailed wealth distributions. Our approach exploits the asymptotic linearity of policy functions and the analytical characterization of the Pareto exponent to make the solution algorithm more transparent, efficient, and accurate with zero additional computational cost. As an application, we solve a heterogeneous-agent model that features persistent earnings and investment risk, borrowing constraint, portfolio decision, and endogenous Pareto-tailed wealth distribution. We show that relaxing the borrowing limit from 25% of annual income to 250% increases inequality by reducing the bottom 50% wealth share from 11% to 6.7% and decreases welfare by 8.2% in consumption equivalent.