Risk estimation and stochastic control of innovation processes

The innovation introduction, no matter whether a product, technology, a method, etc., is being implemented, is connected with considerable risk of investments loss and highly stochastic behaviour, depending on unpredictable factors. It is acknowledged that the innovation passes at least through 6 general stages: 1 - Prestart stage; 2 - Start stage; 3 - Initial expansion stage; 4 - Quick expansion stage; 5 - Stage of reaching liquidity of venture investments; 6 - Stage of project failure and its cancelling. Each state may be refined in details. It is important for the Decision Maker (DM) on one hand to be able to estimate the risk of transitions from a state to state and the probability also for profitable outcome of the initiative - for this purpose a network flow model is proposed; and on the other hand - it is useful if the DM may apply different actions at each stage so that to minimize the losses and maximize the final profit - for this purpose a Markov Decision Process is proposed, which is very closely related to the network flow model and both may be united in a Markov flow.