This is a very important question for anyone who goes away. If מצה needs to be yours to be יוצא the mitzva, when you go away for the seder you may not be יוצא.
The Gemara in Pesachim (38a) states that you cannot be יוצא with matza of מעשר שני if מעשר שני is ממון גבוה which is the way that we pasken. The Gemara asks why? We understand why you aren't יוצא with an Esrog of מעשר שני because it isn't yours and by the 4 minim it says לכם, however by matza it doesn't say מצתכם. The gemara answers that it is learned out from חלה that חלה needs to be משלכם.
The simple reading of the Gemara is that there is a דין of לכם by matza as well learned out from חלה and this is the reason why you are not יוצא with matza of מעשר שני. This is how the Rosh paskens.
However, the Rambam paskens that you are not יוצא with matza of מעשר שני, yet when it comes to stolen matzah he says you are not יוצא because of מצוה הבא בעבירה. The obvious questions is why didn't the Rambam say that you are not יוצא because it isn't yours and matzah needs to be yours. The answer would seem to be that the Rambam holds that matzah doesn't need to be yours.
RYBS explained the Rambam as follows. The Gemara learned out מצה from חלה. However, by חלה there really is no din of לכם. You are חייב חלה even if you use your friends dough. The Rambam understood the Gemara as follows. The Gemara rejected the idea that matza has to be yours because it doesn't say מצתכם. The Gemara learns out a different din from חלה. Namely, that you are not יוצא with matza of מעשר שני just like an עיסה of מעשר שני is not חייב in חלה. The reason for this is that מעשר שני is ממון גבוה, however, not because it isn't yours but because you cannot be יוצא with something that is הקדש. In other words, it is a special din by הקדש and not a general din of לכם. Therefore there is no din by matza that it needs to be yours.
The Taz raises this usse in Shulchan Aruch and answers that the person who gives you the food has the intention of being מקנה the food to you and therefore it would be yours. However, this is actually a מחלוקת in Even Haezer. What happenes if Reuven is eating in Shimon's house and is מקדש Rivka with the food that Shimon gave him to eat? There are 2 opinions whether he is married or not, the question being was Shimon מקנה him the food or not. Therefore on pesach night the host should explicitly be מקנה the matza to his guests.