However I am uncertain as to what extent 'self insurance' reaches in the instance of a hull loss or something like the Dugong occurence in Singapore, but certainly eveything else is covered by self insurance.
For QANTAS to elect to self insure Hulls, Passenger Legal Liability, War Cover and Third Party Liability they would need a war chest that was measured in billions, several billions in fact and the third party element would have to be visible before they can overfly or fly into various foreign territories or ports.
Worst case scenario, a nearly full A380, ($250+Million?) crashes into the CBD of a major city, (Third party exposure in the order of
billions) and all pax die, despite what it says on the ticket, allow about $1Million per seat, after court cases, much, much more in the USA and if QF went into the insurance market and said they would self insure hulls but wanted market cover for pax legal liability and third party they would be politely told to go elsewhere.
Unless they have been very clever at hiding it, I don't think QF have that kind of money.