Here is another look at an answer.
The problem with "my stories" is that I am reticent to claim ownership. Are they really mine?
They are my parents', my aunts' and uncles', my grandparents' stories. Do I ask for them and begin tape-recording, listening diligently? And then what? Would I have what it takes to shape them with the respect and finesse they deserve? Why do it? Can I give my relatives back their own memories? Would I be a writer or a ventriloquist?
Would I be honouring my genealogical history or exploiting my family for material?
I would guess that to a storyteller in the oral tradition, like Dan Yashinsky, stories can belong to one person (or group), but can be told by anyone as long as they are told faithfully. He is quoted as saying,
"Stories show you that other people have traveled before you," he says. "They show you that no matter what is happening in your life, someone else has gone there before you. Someone else has been there, come back, and at least has a good story to show for it."
Some of these stories (like those of my family) have already been told by writers like Andree Aciman in Out of Egypt, Hisham Matar in In the Country of Men, and Lucette Lagnado's The Man in the White Sharkskin Suit. Aciman's memoir beautifully and painfully renders Alexandria and the expulsion of Egypt's Jews, and Matar (whom I have not yet read), tells of the fear of his (non-Jewish) family during Khadafi's rise to power. Lagnado relates the contrast of her father's dashing life in Cairo society till Nasser's rise, and the cost on the family of delaying their departure from Egypt.
Some of my own childhood feels "told" in the first story (about Russian Jews in 1980s Toronto) in Natasha and Other Stories by David Bezmosgis. What my parents may have felt upon their arrival to Canada was projected so intensely on top of my own memories that I found it hard to breathe.
If I am to record the stories I have heard all my life, I must do it soon. These inherited stories are not mine directly, but I am free to try and preserve them or keep them in trust for future generations.
My friend, an Egyptian Christian (Copt), who introduced me to "Out of Egypt" says that even though it is not exactly his story, nothing comforts him and takes him back to his youth like the description of old Alexandria in the novel.
Maybe I won't know who the stories belong to until they are read.