I can see a blue/turquoise painted BMX. The bike has grinding pegs on both the front and rear axles, so it was set up more as a "trick" or stunt BMX over racing or riding.
Curiously, the one brake lever visible goes off in the direction of the back wheel, and I see no trace of a front brake at all. There is also no detangler which means the bike can't do bar spins.
This suggests that it was not a "proper" high-end tricks bike, and was more likely a generic kid's BMX.
I'm sorry that your bike was stolen. And now you either pay for a replacement or struggle with insurance to get a payout which could end up being less than you need for a replacement bike, and may end up costing more than any payout by the time all the clauses are evaluated.
You can try sending the above photo to pawn shops in your area too. I managed to get a stolen digital camera recovered by doing this. Also doing a police report for stolen property will be required for the insurance claim.