In this paper we study the minimization problem of the infinite-horizon expected exponential utility total cost for continuous-time piecewise deterministic Markov processes with the control acting continuously on the jump intensity \(\lambda \) and on the transition measure Q of the process. The action space is supposed to depend on the state variable and the state space is considered to have a frontier such that the process jumps whenever it touches this boundary. We characterize the optimal value function as the minimal solution of an integro-differential optimality equation satisfying some boundary conditions, as well as the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called policy iteration algorithm, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process.

本文研究连续时间分段确定性马尔可夫过程的无限水平期望指数效用总成本的最小化问题，其中控制连续作用于跳跃强度\（\ lambda \）和过渡度量Q的过程。假定动作空间取决于状态变量，并且状态空间被认为具有边界，使得只要接触该边界，过程就会跳转。我们将最优值函数描述为满足某些边界条件的积分-微分最优方程的最小解，以及确定性平稳最优策略的存在。这些结果是通过使用所谓的策略迭代算法，在问题参数的某些连续性和紧凑性假设以及该过程的一些非爆炸性条件下获得的。