Optimal expenditure patterns for risky R&D projects with time‐dependent returns
重新审视了风险研发项目的Lucas模型，利用微分方程理论探索最优支出的新解，发现最优支出随时间的变化与预期回报在函数上相似。
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.