For my part:
Making an attack is process that can be interrupted at several points.
1) Choose the Attack Action
2) Choose a Target
3) Roll the Attack Roll
4) Determine Whether it Hits
5) Deal Damage
Depending on the wording of the ability and the reaction designer's intent, a given reaction can trigger after each of those five points. 
Arcane Riposte specifies that you respond to an "Incoming Attack" with your reaction.
To me, that's after 3 and before 4. Because you could fire off your 
Arcane Riposte the moment you are being attacked whether it's a wild swing or deadly accurate. Thus you can use 
Arcane Riposte to avoid taking damage from an attack by killing someone mid-swing.
My reasoning for this is simple: Reactions acts as Interruptions to the normal flow of action.
The 
Shield spell, for example, would not function if you were to use it after step 5. So Step 5 cannot be the end of the "Triggering Attack". In fact the wording of 
Shield is "When you are Hit" so you're using the 
Shield spell between 4 and 5, specifically, and forcing the gameplay loop back to 4, to see if the attack still hits.
So when I write reactions, sometimes you'll see "When you are attacked" as compared to "When you take damage from an attack" indicating where in the normal flow of action your reaction exists and whether or not the ability can protect you, or others, from taking damage from the attack it interrupts.
It's the Inigo Montoya vs Count Rugen moment. The 
Arcane Riposte stops the attack as long as you get revenge for your father's ignominious death before the strike lands.
		
		
	
	
This moment, right here. The incoming attack is stopped as soon as the counterattack kills the baddie.