Optimal expenditure patterns for risky R&D projects with time-dependent returns

Avi Messica, Israel David

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The basic Lucas model for risky R&D projects is revisited. New solutions for optimal expenditures are explored by exploiting the merits of the theory of differential equations. After applying the calculus of variations, a nonlinear differential equation is presented whose solution provides the optimal control for a constant conditional-completion density function and different time-dependent return models. New, exact, and approximate solutions are presented and discussed. It is found, for the class of risky R&D projects under study, that the behavior over time of the optimal expenditure is functionally similar to that of the expected return.

Original languageEnglish
Pages (from-to)247-254
Number of pages8
JournalR and D Management
Issue number3
StatePublished - 1 Jan 2000

ASJC Scopus subject areas

  • Business and International Management
  • General Business, Management and Accounting
  • Strategy and Management
  • Management of Technology and Innovation


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