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Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations (1403.1217v1)
Published 5 Mar 2014 in math.NA
Abstract: We consider the numerical solution of Hamilton-Jacobi-BeLLMan equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak assumptions, including the case of arbitrary degenerate diffusions. Besides providing a unifying framework that includes several known first order accurate schemes, stability and convergence results are given, along with two different robust error estimates. Finally, the method is applied to a super-replication problem from finance.