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In this paper, we consider the gradual-impulse control problem ofcontinuous-time Markov decision processes, where the system performance ismeasured by the expectation of the exponential utility of the total cost. Weprove, under very general conditions on the system primitives, the existence ofa deterministic stationary optimal policy out of a more general class ofpolicies. Policies that we consider allow multiple simultaneous impulses,randomized selection of impulses with random effects, relaxed gradual controls,and accumulation of jumps. After characterizing the value function using theoptimality equation, we reduce the continuous-time gradual-impulse controlproblem to an equivalent simple discrete-time Markov decision process, whoseaction space is the union of the sets of gradual and impulsive actions.

On gradual-impulse control of continuous-time Markov decision processes with exponential utility