Could you give me some examples and/or references on "risk-averse" loss functions (i.e. penalizing the underestimates more then the overestimates)?
Bayesian Methods for Hackers has a pretty informative chapter on loss functions and touches on this. They provide python function below as an example of a loss function that penalizes overestimates more heavily:
def stock_loss(true_return, yhat, alpha = 100.): if true_return * yhat < 0: #opposite signs, not good return alpha*yhat**2 - np.sign(true_return)*yhat \ + abs(true_return) else: return abs(true_return - yhat)
Note: you don't need to go full bayesian for this chapter to be relevant