When I arrived, Hussein was reading his paper.

【翻译】当我到达时，侯赛因正在看报。

广义上的 read a/one's paper 一般指“读报”，因为绝大部分普通人都能够“读报”，而只有少部分人才可以写出“论文”。若说“读论文”，应换成reading an/his essay， 意义才明确。

When I arrived, Hussein was reading his essay.

【翻译】当我到达时，侯赛因正在阅读他的论文。

如果说：write his paper, revise his paper 等，意思就很明确，就是：“写论文，修改论文”，这时，则不能翻译成“写报纸，修改报纸”了。

看来，词语的“常规用法”和恰当的“动宾搭配”，结合起来理解是关键。

更多例句：

1. Hurstwood quit reading his paper and changed his clothes.  

赫斯渥停止了看报,换上衣服。

来自英汉文学 - 嘉莉妹妹

2. In the front room Hanson was reading his paper.  

在前屋,汉生正在看报。

来自英汉文学 - 嘉莉妹妹

3. Tom went on reading his paper.  

汤姆继续读他的报纸。

4. Three days later he's reading his paper when she walks up behind him and smacks him on the back of the head again with the frying pan。 

三天后，他正在看报纸，妻子走到他身后，又用一只煎锅敲他的后脑勺。

5. Sometimes he looked up at the clock, and then he went back to read his paper. 

他不时地抬起头看看时钟，然后又接着看报纸。