Loss function that penalizes under-predictions more than over-predictions?

Question

I have a regression problem where I am predicting a continuous variable. Loss functions used most often in these cases (RMSE, MAE, etc.) don't treat over- or under- predictions differently.

I am in a scenario where under-predicting would be a much worse outcome than over-predicting.

What type of loss function would appropriately capture this?

Answer 1

Pick an asymmetric loss function. One option is quantile regression (linear but with different slopes for positive and negative errors).