# Why Loss function has to be bounded from below (statistical decision theory)?

In statistical decision theory the loss function $L(\theta, a)\ge-K > -\infty$ is often chosen for technical convenience (e.g. See [1] p.3 ). Can anyone explain why the above condition is convenient, and if it is feasible, provide a simple example.

[1.] James O. Berger, "Statistical Decision Theory and Bayesian Analysis"

• One problem leaps out immediately: you might have a hard time using any procedure that is based on expected loss. You could end up comparing a lot of values of $-\infty$ to each other. More pragmatically, since an infinite loss is unrealistic, why would one want to tackle the technical complications of allowing for it in the first place? – whuber Jan 16 '18 at 17:02