Numerical algorithms for research and development stochastic control models

Chi Man LEUNG, Yue Kuen Kwok

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


We consider the optimal strategy of research and development (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 technological uncertainty associated with the success of the R&D effort and market uncertainty about 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 an impact on the R&D process, 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 depends 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 a firm’s knowledge stock and may even drop to zero when the accumulation level is sufficiently high.

Original languageEnglish
Pages (from-to)3-29
Number of pages27
JournalJournal of Computational Finance
Issue number1
Publication statusPublished - Sept 2014

Scopus Subject Areas

  • Finance
  • Computer Science Applications
  • Applied Mathematics


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