Optimal Investment in Research and Development Under Uncertainty

This paper explores the optimal expenditure rate that a firm should employ to develop a new technology and pursue the registration of the related patent. Our model takes into account an economic environment with indus-trial competition among firms operating in the same sector and in presence of uncertainty in knowledge accumulation. We develop a stochastic optimal control problem with random horizon, and solve it theoretically by adopting a dynamic programming approach. An extensive numerical analysis suggests that the optimal expenditure rate is a decreasing function in time and its sen-sitivity to uncertainty depends on the stage of the race. The odds for the firm to preempt the rivals non-linearly depend on the degree of competition in the market.