Is there any way to remove the stock ticker from Notification Center in iOS5?
Go to Settings > Notifications > Stock Widget and turn it Off.

Notifications for all apps that can display them are managed in Settings. Two built-in apps, Stocks and Weather, get exceptional treatment and show in Notification Center as widgets. In the Notifications Settings, they are listed as Stock Widget and the Weather Widget. 

To prevent an app from displaying in Notification Center, click the app in the list and make sure the option “Notification Center” is set to off.