Ah, here's a minor character that still manages to play a significant plot role.
One really telling thing we learn about the duke is that he does his best to discover and prevent the villainous activity of his son, Lorenzo. By making the audience certain that he is not in league with any of the criminal plots in the play, the duke remains a relatively innocent victim who randomly gets killed while Hieronimo's taking people out. His death helps us to consider the full implications of revenge.
It's worth noting that the duke does help to arrange for his daughter to marry the scoundrel, Balthazar. While it's unclear whether or not he knows Balthazar is a bad guy, the play does cast arranged marriages in a questionable light. We should keep in mind that arranged marriages were the well-established norm for well-born children in this age. Still, the duke's life and death are important factors for you to consider as you form your opinion on how the play portrays arranged marriages.
So what do you think? Did the duke deserve to get stabbed with a pen? Oh yeah, you might also want to consider the whole pen is mightier than the sword thing, too.