Abstract

http://ssrn.com/abstract=1955879
 
 

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Numerical Algorithms for R&D Stochastic Control Models


Chi Man Leung


Hong Kong University of Science & Technology - Department of Mathematics

Yue Kuen Kwok


Hong Kong University of Science & Technology - Department of Mathematics

September 18, 2013


Abstract:     
We consider the optimal strategy of R&D expenditure adopted by a firm that engages in R&D to develop an innovative product to be launched in the market. The firm faces with technological uncertainty associated with the success of the R&D effort and market uncertainty of the stochastic revenue flow generated by the new product. Our model departs from most R&D models by assuming that the firm’s knowledge accumulation has impact on the R&D progress, so the hazard rate of arrival of R&D success is no longer memoryless. Also, we assume a finite life span of the technologies that the product resides on. In this paper, we propose efficient finite difference schemes that solve the Hamilton-Jacobi-Bellman formulation of the resulting finite time R&D stochastic control models with an optimal control on R&D expenditure and an optimal stopping rule on the abandonment of R&D effort. The optimal strategies of R&D expenditure with varying sets of model parameters are analyzed. In particular, we observe that R&D expenditure decreases with firm’s knowledge stock and may even drop to zero when the accumulation level is sufficiently high.

Number of Pages in PDF File: 26

Keywords: stochastic control, R&D model, knowledge accumulation, finite difference schemes

JEL Classification: C73, L13, O33

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Date posted: November 30, 2011 ; Last revised: October 16, 2013

Suggested Citation

Leung, Chi Man and Kwok, Yue Kuen, Numerical Algorithms for R&D Stochastic Control Models (September 18, 2013). Available at SSRN: http://ssrn.com/abstract=1955879 or http://dx.doi.org/10.2139/ssrn.1955879

Contact Information

Chi Man Leung
Hong Kong University of Science & Technology - Department of Mathematics ( email )
Lift 25-26
Clear Water Bay, Kowloon
Hong Kong
Yue Kuen Kwok (Contact Author)
Hong Kong University of Science & Technology - Department of Mathematics ( email )
Clearwater Bay
Kowloon
Hong Kong
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