Numerical Algorithms for R&D Stochastic Control Models

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