Median predictive cost of error with an asymmetric cost function

The problem of reducing predictive cost is considered in the case when the cost of error function is not symmetric and the optimality criterion is the minimization of the median cost of the error of prediction. Examples are given and comparisons made with the usual solution based on the minimization of the mean cost. In the case of a Gaussian process, the median solution is found to be a simple additive adjustment to the predictive mean, and far easier to compute than the solution based on expected cost.