2018/02/20 by Olivier Bokanowski, Bokanowski, Olivier, Athena Picarelli +3
Economics, Econometrics and Finance · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1802.07146
openalex publication_date 2018/02/20 · openalex created_date 2022/08/24 · openalex updated_date 2026/07/28
We study a second order BDF (Backward Differentiation Formula) scheme for the\nnumerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations.\nThe scheme under consideration is implicit, non-monotone, and second order\naccurate in time and space. The lack of monotonicity prevents the use of\nwell-known convergence results for solutions in the viscosity sense. In this\nwork, we establish rigorous stability results in a general nonlinear setting as\nwell as convergence results for some particular cases with additional\nregularity assumptions. While most results are presented for one-dimensional,\nlinear parabolic and non-linear HJB equations, some results are also extended\nto multiple dimensions and to Isaacs equations. Numerical tests are included to\nvalidate the method.\n