Forecast and decision horizons in a commodity trading model

Forecasts of demands or prices become increasingly unreliable as the future becomes more distant. It is, therefore, beneficial to show that optimal decisions during an initial time interval are either partially or wholly independent of the forecasted data from some future time onwards. Using a commodity trading model as an example, we obtain conditions that allow us to make optimal buying and selling decisions for a commodity in some initial time interval without knowing its price forecast beyond some future time. Such an initial time interval is called a decision horizon and the time up to which the forecasted data is required to make the optimal decisions during the decision horizon is called a forecast horizon. We use the maximum principle to solve the example and show that the decision and forecast horizons in the problem arise from lower and upper bounds imposed on the on-hand inventory of the commodity.