In [Azimzadeh, P., and P. A. Forsyth. "Weakly chained matrices, policy iteration, and impulse control." SIAM J. Num. Anal. 54.3 (2016): 1341-1364], we outlined the theory and implementation of computational methods for implicit schemes for Hamilton-Jacobi-Bellman quasi-variational inequalities. No convergence proofs were given therein. This work closes the gap by giving rigorous proofs of convergence. A point of difficulty in the analysis is that a standard application of the Barles-Souganidis framework (BSF) requires a stronger comparison principle than that which is available in the literature. By introducing a stronger notion of consistency than that which is posed in the BSF, we are able to prove convergence relying only on a well-known comparison principle. Our results are robust in that we do not assume a specific form for the intervention operator.

Joint work with Erhan Bayraktar and George Labahn. Speaker(s): Parsiad Azimzadeh (UM)