A controlled jump discounted model with constraints

In the problem under consideration the given functionals of the trajectories must satisfy a system of inequalities. As usual, a construction of control strategy is required to ensure attainment of the extremal value of the criterion.
The paper provides an investigation of the space of strategy measures; necessary and sufficient optimality conditions are obtained, an algorithm of constructing optimal strategy for the Markovian case is developed, and an informative exactly solved example is given.