【摘要】 以随机分析的知识和最优控制理论为基础,推广了一类带停时的奇异型随机控制中的折扣费用模型,主要在受控状态过程中增加了漂移因子和扩散因子,使其为一随机微分方程的解,并将费用函数一般化.通过求解一组变分方程,证明了最优控制及最优停时的存在性,并给出了最优费用函数的解析表达式.更多还原

【Abstract】 Based on the stochastic calculus and the classical theory of optimal control,this paper generalizes a class of the discounted model of singular stochastic control with stopping time.Drift and diffusion coefficients are introduced into the controlled states to make them the solution of a stochastic differential equation.Meanwhile,the cost function is also generalized.By solving a variational equation,we prove the existence of the optimal control and the optimal stopping time.Moreover,we derive the explicit form for the optimal cost function.更多还原