A Stochastic Model of Consumer Behavior and Optimal Advertising

A stochastic consumer behavior model is constructed transforming Nicosia's (Nicosia, F. M., 1966. Consumer Decision Processes. Prentice-Hall, Englewood Cliffs, New Jersey.) postulates into probability hypotheses. Nicosia's deterministic model is obtained in the mean evolutions and variance-covariances, defined by a system of linear differential equations obtained. This system, forming together with mean evolutions a closed system of five simultaneous differential equations is studied for stability, to devise optimal communication strategies and for suggesting an estimation technique.