关于脉冲消费控制策略的最优随机问题研究

讨论了一类随机控制问题,其脉冲消费控制策略受控于一混合过程——几何布朗运动和泊松过程.在基于获得效用函数期望值的最大值这一目标下,利用变分不等式和随机积分理论,获得了最优消费控制策略及最优值函数所满足的定理,并进一步针对具体的参数,给出了其数值计算结果.

Discussion on a Class of Impulse Consumption Control Strategy of Optimal Stochastic Problem

A stochastic control problem is discussed.The impulse consumption control strategy of the problem is governed by a mixed process-geometrical Brownian motion and a Poisson process.In order to achieve the maximum of the objective function defined by the expectation of a utility function,by using the variational inequalities and stochastic calculus control theory,the optimal consumption strategy and the theorem that the optimal value function satisfy are obtained.Furthermore,its numerical computation results for some explicit parameters are calculated.