Stochastic dynamic pricing: Utilizing demand response in an adaptive manner

Dynamic pricing to residential customers has been proposed recently, as extensions of static network utility maximization problems. Those deterministic models do not exploit the refined information as time advances. To address this issue, we formulate a stochastic dynamic pricing framework, in which we show the existence of an optimal price process that incentives the agents to choose the socially optimal decisions. We develop a distributed algorithm and investigate the information structure of the involved stochastic processes via a numerical example, which also illustrates the advantage of stochastic dynamic pricing over deterministic dynamic pricing.