Abstract The paper is concerned with a stochastic inventory models for continuously deteriorating items with price dependent demand’s intensity, zero ending inventory, and non-zero lead time. We assume that demand process is a compound Poisson with continuous increments or is described by a Brownian motion process. The objective of this paper is to determine the selling price and lot-size maximizing the average profit per unit time for a lot size large enough. We prove that the main part of the mean cycle time as lot-size tends to infinity is the same as for deterministic demand. We obtain the equations for optimal lot-size and time varying selling price.