Innovation diffusion uncertainty,advertising and pricing policies |
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| Institution: | 1. McDonough School of Business, Georgetown University, 37th and O. Street N.W., Washington, DC 20057, USA;2. R.H. Smith School of Business and Management, University of Maryland, College Park, MD 20742-1815, USA;3. Office of the Comptroller of the Currency, Risk Analysis Division, Mail Stop 2-1, 250 E Street SW, Washington, DC 20219, USA;1. School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK;2. Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, ROC;3. Department of Statistics, Purdue University, West Lafayette, IN 47907-2068, USA;1. Maastricht University, School of Business and Economics, Maastricht School of Management, The Netherlands;2. Institute for the Study of Labor (IZA), Germany;3. Department of Economics, University of Paderborn, Germany;4. Center for International Economics, University of Paderborn, Germany;1. Department of Mathematics, China University of Mining and Technology, 221116 Xuzhou, China;2. Department of Mathematics, Zhengzhou University of Light Industry, 450002 Zhengzhou, China |
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| Abstract: | 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 pricing) are viewed as a value additive sequence of nested real options. We present closed-form analytic results regarding the optimal policies. Simulations provide a numeric insight to the models' behavior. |
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