Optimal Funding Paths for a Class of Risky R&D Projects

The problem of financing risky R&D projects over time has been stated as an optimal control problem by Hess [Hess, S. W. 1962. A dynamic approach to R&D budgeting and project selection. IRE Transactions on Engineering ManagementEM-9 (December) 170–178.], Lucas [Lucas, Robert E. 1971. Optimal management of a research and development project. Management Sci.17 (11, July) 679–697.], and Kamien and Schwartz [Kamien, M. I., N. L. Schwartz. 1971. Expenditure patterns for risky R&D projects. J. Appl. Probab.VIII (1, March) 60–72.]. In this paper, the model is extended to allow the possibility of time dependent returns. The authors restate the problem as a finite horizon continuous time dynamic programming problem, and demonstrate uniform convergence to a unique, autonomous (infinite horizon) solution for the present value of the project and optimal spending rate as a function of expended effort. Further conclusions are shown for the time dependent model with exponential completion probability and for the time independent model.