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

We analyze stochastic dynamic multi-product pricing models for durable goods and consider a single advertising channel to promote all types of products. We include general adoption effects, unit costs as well as inventory holding costs. In case of isoelastic, exponential and linear demand, we derive solution formulas for the expected profit, the optimal feedback prices for all types of products, and the optimal advertising rate. In order to evaluate optimally controlled sales processes over time, we use efficient simulation techniques. Moreover, for the case of exponential demand, we demonstrate how to include risk aversion in the model.