This paper is concerned with a stochastic inventory models for a continuously deteriorating product. We consider an observed stock level process as a diffusion process where the drift and diffusion coefficients are linear functions of the stock level. Lot size maximizing the expected profit per unit time for large lot sizes is obtained. In case of a price-dependent intensity of customers’ flow and a compound Poisson demand a model of a dynamic price control is proposed and lot size maximizing the expected profit at a fixed time interval is found. Currently, dynamic price management is of highly practical interest due to advances in digital technologies.