Iterative spectral methods for Hamilton-Jacobi-Bellman quasi-variational inequality in finance

This study proposes a novel computational scheme for utility-maximization problems involving optimal stopping, formulated as Hamilton-Jacobi-Bellman quasi-variational inequalities. The methodology integrates Gauss-Lobatto-Legendre spectral discretization with a penalization method and is solved efficiently via policy iteration. We establish the convergence of the penalized scheme and verify the effectiveness and robustness of the framework through a series of numerical experiments.