We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results by an application to the optimal consumption rate from an economic quantity.

We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. Finally, we illustrate our findings with an example.

In this paper we introduce a new technique to construct unique strong solutions of SDE's with singular coefficients driven by certain Lévy processes. Our method which is based on Malliavin calculus does not rely on a pathwise uniqueness argument. Furthermore, the approach, which provides a direct construction principle, grants the additional insight that the obtained solutions are Malliavin differentiable.Mathematics Subject Classification (2010) 60H10 · 60H15 · 60H40.

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