Kurushima Aiko

We consider a gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We show, under natural conditions on the system primitives, the existence of a deterministic stationary optimal policy out of a more general class of policies that allow multiple simultaneous impulses, randomized selection of impulses with random effects, and accumulation of jumps. After characterizing the value function using the optimality equation, we reduce the gradual-impulse control problem to an equivalent simple discrete-time Markov decision process, whose action space is the union of the sets of gradual and impulsive actions.

In this paper, we present a new monotone approximation of a given real-valued Carathéodory function on the product X × A of Borel spaces, where A is also compact. We demonstrate its application by providing a self-contained and elementary proof of a result of A. Nowak in discrete-time Markov decision processes.