Dead battery after alarm went off

Yesterday at 05.30 the alarm in my three month old Portofino apparently went off. I have no idea why (this is the third false alarm). I was asleep of course and never heard it. Car in in a garage, so no wind either.

Went to the car at 16.00 and found the alarm system was off and I could not open the door. Could not charge the battery with the conditioner either as it kept flashing red. Rang the dealer and a technical peron came to my house (the dealer is ten minutes away). He got the door open manually and started the car with a booster. Subsequently he took the car to the dealer to check why this happened. No word yet.

Anyone else had the same experience? Would an unattended alarm exhaust the battery? How come the car ran (seemingly fine) after being charged with a booster battery? Should I insist on a new battery if they re-charge this one? What could be triggering the alarm so often?