Journal of Computational Finance

Numerical algorithms for research and development stochastic control models

Chi Man Leung and Yue Kuen Kwok


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.

To continue reading...

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an indvidual account here: