In my experience (which led me to pay for luggage insurance) the airlines are cooperative about loss/damage provided that the luggage is insured with someone else or with a documented value from before the trip. If not — if you tell them after the fact that an absent suitcase was valuable and they're on the hook ­— they'll drag their feet endlessly.

It took me ten months to give up, gnash my teeth and take out insurance, so if your experience will be like mine you have another eight months of frustration ahead of you. It sucks.