Modeling Stochastic Innovation Races

We consider a firm moving towards a stochastic final destination, to be chosen from a discrete set after a decision period. The decision period itself may be deterministic or stochastic. We assume the firm can move at variable innovation (R&D) speed associated with a monotone nondecreasing variable cost, and it can also stop and move anywhere. There is a fixed cost per time unit "carried" by the firm as well, associated with keeping at the knowledge (technology) frontier. We investigate various types of the firm's optimal trajectory in the R&D race during the decision period.