Continuous Time Research and Development Investment and Innovation: Effects on Price and Dividend Paths - Thomas A. Rietz (Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, 1989)
Here, I solve a general equilibrium, stochastic, dynamic control problem. In it, an agent who owns a productive asset decides how much of a non-storable good to consume and how much to invest in research and development. Combined, two features distinguish this from previous work. First, the agent maximizes lifetime expected utility (instead of profits or income). Second, the investment level affects the probability of a research and development innovation which would make future dividends jump. Dividend evolution is represented by a continuous time Poisson process with the jump probability depending on the investment level. In equilibrium, the agent chooses the investment level to give an optimal expected innovation rate. This results in endogenously chose, stationary growth rates in asset dividends and prices. These non-stationary price and dividend paths are of a type that Marsh and Merton (1986) predict will violate variance bounds tests such as Shiller's (1981). However, they are not subject to Shiller's (1986) criticism of Marsh and Merton, because they result from a general equilibrium with all agents behaving optimally and rationally.
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