Loss functions discussion

[markbneal]

At the end of chapter 3.1, the last sentence is:

And in decision theory, one seeks to minimize one's expected loss

Coming from an economics perspective, we seek to maximise gain. from a maths perspective minimising F(x) is the same as maximising G(x) = -F(x). Is this worth a footnote?

Then in section 3.2, paragraph four states:

Here, of course, instead of minimizing expected losses, we want to maximize the expected gain.

Then it is suggested to use the mode. I think the point is that whether the problem is max gain or min loss makes no difference - in this case the binary loss (or gain) function is why the mode is now relevant. Perhaps this could be made clearer?

Ps - I found this diagram helpful to clarify for me. https://www.stat.auckland.ac.nz/~brewer/stats331.pdf