The Outlook object model doesn't provide anything for that out of the box. The only possible solution is to use the NameSpace.GetSharedDefaultFolder method which returns a
Folder object that represents the specified default folder for the specified user. So, you may try to retrieve one and check whether it is yours.
However, you may try using a low-level API on which Outlook is based on - Extended MAPI. You may try to check out permissions of the folder, see Update Folder Permissions using VBA for more information.