On optimal leader's investments strategy in a cyclic model of innovation race with random inventions times

In this paper, we develop a new dynamic model of optimal investments in R&D and manufacturing for a technological leader competing with a large number of identical followers on the market of a technological product. The model is formulated in the form of the infinite time horizon stochastic optimization problem. The evolution of new generations of the product is treated as a Poisson-type cyclic stochastic process. The technology spillovers effect acts as a driving force of technological change. We show that the original probabilistic problem that the leader is faced with can be reduced to a deterministic one. This result makes it possible to perform analytical studies and numerical calculations. Numerical simulations and economic interpretations are presented as well.