Innovation diffusion uncertainty, advertising and pricing policies

We develop and analyze a normative and structurally stochastic model of innovation diffusion by depicting the market at an aggregate level. Model dynamics are defined through the flow pattern of individuals that move from the innovation unaware stage, to the innovation aware, and ultimately to the adopter stages. The stochastic evolution of this stage-wise transition unfolds according to tractable stochastic processes and is influenced by such factors as price, word of mouth, and advertisement efforts. In this environment, techniques of contingent claims analysis and stochastic control theory are employed to obtain optimal pricing or advertising policies that maximize the value of the innovation. To account for their optimal adjustment over time, these policies are modeled as positive real-valued adapted processes. Given this setting, policy adjustments over time (i.e. advertising or prices) are viewed as a value additive sequence of nested real options. We present closed-form analytic results regarding the optimal policies. Simulations provide a numerical insight to the models' behavior.