Summary
It is supposed that the behaviour of a process with a single random jump can be controlled by selecting Radon-Nikodym derivatives, that determine probability measures describing when the jump happens and where it goes. By observing that the minimum cost function is a “semi-martingale speciale” a dynamic programming minimum principle for the optimum control is obtained. An “adjoint variable” is introduced and shown to satisfy a certain differential equation, and the results are extended to multi-jump processes.
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Davis, M., Elliott, R. Optimal control of a jump process. Z. Wahrscheinlichkeitstheorie verw Gebiete 40, 183–202 (1977). https://doi.org/10.1007/BF00736046
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DOI: https://doi.org/10.1007/BF00736046