Mark Harrigan's ability instructs you to draw a card when "damage is placed on a card you control." Does Mark's investigator card count as a card you control for this purpose?
Do you "control" your investigator card? (Mark Harrigan question)
Going off the "Ownership and Control" entry in the RRG, I would say that yes, it does.
Your investigator card is in your play area at the start of the game (setup step 1), making you the owner of it. Since it is in play and "cards by default enter play under their owner's control", it seems to me that unless there is specific contradictory text somewhere you do control your investigator card.
It is a card. You control it. Q.E.D., it is a card you control. 
From the FAQ:
Quote(1.2) Triggered Abilities
An investigator is permitted to use triggered abilities ([Free], [Reaction], and [Action] abilities) from the following sources:
• A card in play and under his or her control. This includes his or her investigator card.
If you didn't control your investigator card, you wouldn't be allowed to trigger the abilities written on it, including Mark's reaction.