I sometimes hear Japanese people use "my" and "your" in ways that sounded strange to me, though I couldn't quite place why. I believe it's a transliteration(直訳) for sentences like, "あなたの手紙を待っています。" This becomes, "I am waiting for your letter", which is usually incorrect, and 不自然。 It's more appropriate to say, "I am waiting for a letter from you".
The listener needs to know about the item being discussed before you can use "my, "your", "his", etc.
POちゃん: I am going to have my birthday party!
私の誕生日パーティを開きます。
BH君 : ....

。。。?

そのパーティを紹介しないと、聞いてる人の頭の中にまだ存在してないわけ。紹介をすると聞いてる人の頭の中に存在しているから、「my」を使ってもOKです:

POちゃん: I am going to have a party. My party will be lots of fun.
パーティを開きます!そのパーティはとても楽しいでしょう。
BH君: Sounds great! Can I go too?
いいですね。僕も参加してもいい?
POちゃん: Sorry, you are not invited.
ごめんなさい、あんたを誘ってないわ。
BH君: ...
。。。 orz

Here's another example:
A君 : When will you buy your car?
マイカーはいつ買うんですか
B君 : What? I don't have a car, but I want to buy one.
え?車ないんですが、買いたいと思っていますよ。
Here, it would be more appropriate to say, "when will you buy a car?", since the listener does not have any car that he's purchasing, and if he did, it's not his car yet, and thus can't be called "your".
This is all analogous to "the" and "a", the "definite" and "indefinite" articles. Use of "your" corresponds to use of "the". In both cases, the listener must be aware of the object being discussed. If not, "a" should be used.
A deeper discussion of "the" vs "a" requires a whole new 日記。。。 (coming soon!)

