Abstract
This paper explores the optimal expenditure rate that a firm should employ to develop a new technology and pursue the registration of the related patent. We consider an economic environment with industrial competition among firms operating in the same sector and in the presence of uncertainty in knowledge accumulation. We tackle a stochastic optimal control problem with random horizon and solve it theoretically by adopting a dynamic programming approach. An extensive numerical analysis suggests that the optimal expenditure rate is a decreasing function in time, and its sensitivity to uncertainty depends on the stage of the race. The odds for the firm to preempt the rivals nonlinearly depend on the degree of competition in the market.
Highlights
The decision to develop a new technology and -once it has been fully developedthe selection of the appropriate time for taking out a patent are very complex issues
The introduction of a stochastic horizon in the problem invalidates a great part of dynamic programming theory as commonly known in the literature. To deal with this point we rely on a result recently proved in [7], which formalizes a Dynamic Programming Principle (DPP) for a wide class of stochastic control problems with exit time
Gathering the evidence and the regularities arising from the simulation we can characterize qualitatively the firm’s behavior in the race from two points of view, namely the expenditure rate dynamics and the odds
Summary
The decision to develop a new technology and -once it has been fully developedthe selection of the appropriate time for taking out a patent are very complex issues. We face the issue of the optimal selection of the expenditure rate to be employed by a firm to develop R & D policies as a stochastic optimal control problem. The introduction of a stochastic horizon in the problem invalidates a great part of dynamic programming theory as commonly known in the literature To deal with this point we rely on a result recently proved in [7], which formalizes a DPP for a wide class of stochastic control problems with exit time. A numerical algorithm is provided, and a sensitivity analysis of the optimal expenditure rate is presented This numerical scheme is based on the finite difference discretization of the HJB equation, coupled with a fixed point scheme to deal with its non-linearity.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
