Discounting a mean reverting cash flow

Cash flows are often modeled using the random geometric growth model (geometric Brownian motion). One of the reasons for using this model is that it is simple to implement and it is a reasonable approximation to random growth cash flows such as stock prices. For this model the volatility of the cash flow grows multiplicatively over time. This multiplicative characteristic is shared by the usual form of discounting. That is, when discounting the discount factor is generally being compounded over time. This compounding is usually nothing more than multiplications of single period discount factors. Thus, the geometric characteristic of discounting relates with the geometric growth characteristic of the random geometric growth model.