There are 3 nouns in this sentence.
One of them Asia is a proper noun because it describes an object which exists alone (there is only one continent called Asia in the world).
The other nouns are not proper (they are called common nouns) because they describe objects which can be multiple.
There are more than one continents.
World seems to be proper noun at the first look, but although we live only on one world we can imagine that there are other worlds for example in outer space. So there is no reason to treat the noun world as a proper one.
Usually the nouns can be distinguished when you look at them because in most languages proper nouns start with a capital letter while common nouns don't, so the correct sentence would be:
Asia is the largest continent in the world.