Stochastic dynamic multi-product pricing with dynamic advertising and adoption effects

In this article we analyze stochastic dynamic multi‐product pricing models for the sale of durable goods. In addition, we consider a single advertising channel to promote all types of products. We also include product‐specific unit costs, inventory holding costs as well as general adoption and saturation effects in the demand. For the case of isoelastic, exponential and linear demand, we derive solution formulas for the expected profit, the optimal prices of all types of products, and the optimal advertising rate. Efficient simulation techniques are used to evaluate optimally controlled sales processes over time. Moreover, for the case of exponential demand, we demonstrate how to include constant absolute risk aversion in the model.