YOU have absolute control over where you live.
In this regard, I beg to differ. Sometimes an economic or work situation may dictate that one live in an area which is not up to their standards or preferences. At times, I've been forced to live in areas with higher crime or possibility of break-ins and thefts than I'd like for one or another reasons. While it's a nice illusion, sometimes we really don't have all the control over our circumstances that we'd like to imagine we do.
OP, I can only tell you how I've reacted in similar situations.
1: ~1 am, I was moving into a new apartment and had the door open while I was running back and forth to the moving van. My dog starts barking and growling and I see a very large individual silhouetted in my doorway. Turns out it was my 5'7" neighbor asking when I was going to move the van, as he had to go into work in the morning. Funny what tricks light and fear will pull on your eyes... I answered the door after drawing my gun, but had it hidden behind my hip, so hopefully he never noticed it. I told him I would move the van shortly so he wouldn't have a problem leaving in the morning. We made some small talk and he went back to his apartment and I finished moving.
2: I was asleep on my couch around 2 in the morning when someone barged in through my unlocked front door. Turns out it was a drunk friend of my roommate, who was in the habit of leaving the doors unlocked. To be honest, I was startled out of sleep and my first reaction was to yell at him, not go for my shotgun (which was upstairs in my closet, anyway). He very quickly identified himself as a friend of my roommate, who came in about a half hour later and apologized for the whole incident.
In my opinion, while it may be prudent to go armed in your own home, it's far more likely that someone's intentions are benign or simply misinformed. I wouldn't suggest unleashing the "hounds of hell" or even showing a gun. I think dogs are the best home defense/early warning system in existence, and that's in addition to being great companions. I recommend a dog, backed up by a discerning, armed human.
I think merely mentioning the situation to your landlords is sufficient to handle the incident. Perhaps you might request that they inform you if such a thing is to occur again, in order to save undue worry or stress on yourself. No mention of guns, going rambo, hounds of hell, etc. need occur.