Numerical Algorithms for R&D Stochastic Control Models

26 Pages Posted: 30 Nov 2011 Last revised: 16 Oct 2013

See all articles by Chi Man Leung

Chi Man Leung

Hong Kong University of Science & Technology - Department of Mathematics

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: 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.

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

JEL Classification: C73, L13, O33

Suggested Citation

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

Chi Man Leung

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Rm. 3461, 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, 999999
Hong Kong

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
79
Abstract Views
870
Rank
555,299
PlumX Metrics