Rewrite the positive part function $\max(A-B, 0) = (A-B)^+$ as the difference of indicator functions

Question

Rewrite the positive part function $\max(A-B, 0) = (A-B)^+$ as the difference of indicator functions. This identity is quite useful when working with pricing derivatives (call options) as the non-linear payoff becomes linear.

Answer 1

$$\max(A-B, 0) = A 1_{A - B \geq 0} - B 1_{A-B \geq 0}$$ Proof is by verifying equality for both cases $A \geq B$ and $A < B$