We construct an anisotropic, degenerate, fractional operator that nevertheless satisfies a strong form of the maximum principle. By applying such an operator to the concavity function associated to the solution of an equation involving the usual fractional Laplacian, we obtain a fractional form of the celebrated convexity maximum principle devised by Korevaar in the 80’s. Some applications are ...

In this paper, an optimal singular stochastic control problem is considered. The state process is described by a non linear stochastic differential equation. The variation of the control variable is bounded. For this model, it is obtained a general stochastic maximum principle by using a time transformation. This is the first version of the stochastic maximum principle that covers nonlinear cas...