Have been thinking about this a lot recently. Why does God not only allow Satan to exist but also allows him to be abroad?
It comes down to reasoning. God could have made angels and people that had to love him. But instead, he gave both free will so they could choose to love him.
Say you were to marry. Would you prefer someone who had to marry you or someone who choose to marry you?
In the beginning the angels had to show themselves worthy of heaven with God. Satan, a 'top' angel, had free will, just as had all the others. He choose not to obey and one third (I think) followed him rather than choosing to love and obey God. Such were the angels created that they knew exactly what they were doing and would never change their choice.
The very same free-will was/is given to man. And, just as Satan was allowed tempt the angels, so too is he allowed tempt mankind. This way, not only have mankind to choose God, but they have to pass many temptations throughout their lives to do this.
Man is however 'luckier' that the angels. Man can repent, change minds throughout his or her life.
As for 'abroad,' well didn't Pope Leo XIII tell us god gave Satan extra freedom to tempt mankind. Matto is correct in pointing out the Book of Job as illustrating the above, where God allowed Satan greater powers to tempt Job. Unsuccessfully I might add.