Any dynamic pricing model requires establishing how demand responds to changes in price. This paper is dedicated to mathematical models of monopoly systems. Strong assumptions are made to obtain tractable models. While such mathematical models can hardly represent real-life situations, they help understanding the relationship between price and customers’ purchasing behavior. Two mathematical models are presented: (i) A stochastic dynamic pricing model for time dated items without salvage values; (ii) A stochastic dynamic pricing model for time dated items with salvage values. We limit ourselves to time dated items with no supply option in monopolistic environments with myopic customers.