The character arc for Ash through House Valerius is to become his own person, able to make his own decisions and account for his actions. That may sound a bit strange, since the character is in his late twenties, but in the terms of the culture I created for the book, that makes him the equivalent of a teenager so I think it holds up.
At the beginning, the majority of the other characters, to one extent or another, view Ash as a reflection of the older members of his family, primarily his father and his uncle. I tried to reflect this in the way many of those characters address him in conversation. Others, such as those closest to him, have a tendency to treat him as a child, yet to prove his worth.
As mentioned elsewhere, Ash Valerian is, for all intents and purposes, an idealized version of myself. Technically I am a bit older than he is now (we were the same age when I first started writing the series) but there are still enough similarities for people to comment on.
If there is one quality I would hope I share with him it is his loyalty to his friends.