Miko vs. the stray cat

This mangy black stray cat has been coming around my apt EVERY DAY for the past few weeks. She just sits outside my window (I live on the 1st floor) and it totally freaks Miko out. Miko starts racing back and forth from window to window and hissing at the other cat. But the stray has gotten even more aggressive lately. It's started jumping up and clinging to the ledge outside my window, getting right up in Miko's face! It has NO respect for Miko's territory. The other day my window was open a crack somehow and I swear the cats were trying to push it open more. (it slides sideways, so they totally could have done it). They almost got at each other and I had to tear Miko away. I also think the stray has shredded my porch screen doors from the outside. (not that I really care about this apt, but I better not get charged for that damage!). I don't know what to do!!! I'm sure it's not good for Miko's health to be agitated like that every day. It also makes her get more aggressive with me, and I have the scratches to prove it. The stray cat is scared of me, so if I go outside I can usually chase it off. I also try to toss Miko in the windowless tatami room until she calms down. There's a part of me that is of course tempted to feed the stray cat, since she looks like she's wasting away. But then she might NEVER leave. And I can't take in another cat at this point. (Especially since Miko seems to HATE her). Well, Miko and I are out of here in 2 months. In the meantime, any advice from cat people?