In this paper, we formulate a stochastic model of consumer behavior with repeat purchases and imperfect information. By applying the Maximum principle to the defined model, we determine the optimal dynamic strategy of price, advertising investment and product quality when the lifetime of the product has an exponential distribution and the repeat purchase probability is smaller than 0.5.
EL OUARDIGHI, F. and TAPIERO, C. (1996). Optimal Advertising and Signal Reliability. ESSEC Business School.