IDEAS home Printed from
   My bibliography  Save this paper

Dynamic Model of Innovation: Optimal Investment, Optimal Timing, Market Competition


  • A.M. Tarasyev
  • C. Watanabe


A dynamic model of investment process for a technology innovator in a market environment is designed. The "light" dynamics of the active innovator is described by the system of exponential trajectories in which one can quickly change growth parameters. It is assumed that the innovator operates in the inert market environment which can be presented by "heavy" exponential trajectories. The growth parameters of the market trajectories vary slowly and can be identified to some accuracy in the dynamic process of econometric observation basing on information of the current technology stock (the average market technology stock) and its rate (the average market technology rate). The model consists of three decision making levels for dynamical identification, optimization of the commercialization time and optimal control design. On the first level the innovator makes assessment for the current commercialization time using econometric characteristics of the current level of the market technology stock and the market technology rate. Since the market environment is inert and its acceleration (the second derivative) is small then information about the market technology stock (current position) and the market technology rate (current first derivative) gives an opportunity to estimate exponential parameters of the market growth trajectories, to forecast the market commercialization time and indicate its sensitivity. On the second level the innovator optimizes its commercialization time basing on its own current technology stock and taking into account the forecast of the market commercialization time. Two scenarios are possible for the innovator: the "slow" scenario with "large" time of innovation is oriented on the local extremum with usual level of sales of invented products, the "fast" scenario with "small" time of innovation maximizes the early level of innovation with bonus sales due to the market overtaking. On the third level the innovator solves an optimization problem for the investment policy basing on information about the chosen scenario, the commercialization time, and the difference between the achieved technology stock and the demanded technology stock for starting commercialization. Dynamical optimality principles for optimizing discounted innovation costs on investment trajectories are used for finding the optimal investment plan and designing optimal feedback for its realization. Properties of sensitivity and robustness are investigated for the optimal profit result and innovation feedbacks.

Suggested Citation

  • A.M. Tarasyev & C. Watanabe, 2000. "Dynamic Model of Innovation: Optimal Investment, Optimal Timing, Market Competition," Working Papers ir00003, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir00003

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:iasawp:ir00003. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.