带漂移因子及停时的最优脉冲随机控制问题

摘要

By introducing a drift parameter into the controlled state governed by a Poisson process, we formulate an unsymmetrical impulse optimal stochastic control problem. The stopping time is originally introduced into the objective function. By utilizing both stochastic calculus and the classical impulse control theory, we give a set of sufficient conditions for its solution in terms of optimal return function. Moreover, we also derive its optimal control strategy and explicit form of optimal return function under some conditions.%通过把漂移参数引入到受控于Poisson过程的状态结构中,本文建立了一非对称型最优脉冲随机控制模型.在此模型的目标函数中,首次引进了停时因素.利用随机积分及脉冲控制理论,我们不但给出了最优回报函数应满足的充分性条件,而且在一定条件下得出了其显解及相应的最优控制策略.