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

Carole Aldrich and Thomas E. Morton
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Carole Aldrich: Graduate School of Business Administration, Duke University
Thomas E. Morton: Graduate School of Business, University of Chicago

Management Science, 1975, vol. 21, issue 5, 491-500

Abstract: 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 Management EM-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.

Date: 1975
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