Once upon a time, major insurance companies (State Farm, Progressive, etc) covered HDPE's because of the "driver safety/education" loophole. Not anymore. They've all wised up. Just about all of them have fine prints somewhere that excludes coverage during HPDE's. Don't assume that you're covered even if your agent says you are.

Here's a good article about it: Racetrack coverage

Get track-specific insurance as mentioned above!

EDIT: link posted above was for the cliff notes. Here's the complete NY Times article