Primal‐dual methods for the computation of trading regions under proportional transaction costs

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non‐smooth time‐dependent Hamilton–Jacobi–Bellman equation is solved by regularization and the application of a semi‐smooth Newton method. Discretization in space is carried out by finite differences or finite elements. Computational results for one and two risky assets are provided.