Q:

simplifying $\min(\max(A,B),C) $

In a larger problem, I have to make use of the following
$$\min(\max(A,\ B),\ C)$$  
Please how do I simplify?

A:

If you wanna use the notation in stochastic caculus I saw sometimes, $max(A,B) = B + (A-B)_+$, then $$min(B+(A-B)_+, C) = C - (C - B - (A-B)_+)_+$$

