Capacity expansion under stochastic demands

The authors consider the problem of optimally meeting a stochastically growing demand for capacity over an infinite horizon. Under the assumption that demand for product follows either a nonlinear Brownian motion or a non-Markovian birth and death process, they show that this stochastic problem can be transformed into an equivalent deterministic problem. Consistent with earlier work by A. Manne, the equivalent problem is formed by replacing the stochastic demand by its deterministic trend and discounting all costs by a new interest rate that is smaller than the original, in approximate proportion to the uncertainty in the demand.