This part:
What do I need to be careful about when purchasing umbrella insurance?
When you purchase an Umbrella policy, your Umbrella insurance company will require you to maintain specific minimum limits of liability coverage on all of your underlying policies, i.e. your auto insurance, homeowners insurance, boat insurance etc. It will be your responsibility to maintain these underlying required limits. In the event of a liability claim covered by your primary auto, home, or other policy, your Umbrella policy will respond after the primary policy limits are used up. If you fail to maintain the minimum required limits on your primary policies, you will end up with a coverage gap.
For example, assume that your Umbrella insurer requires that you maintain at least $500,000 of liability coverage on your homeowners policy, but you only purchase $300,000 of liability coverage on your homeowners policy. In the event of a covered homeowners liability claim, your homeowners insurer would pay the first $300,000 (your policy limit), but your Umbrella insurer would only begin paying after the first $500,000. Your Umbrella policy would respond only after the first $500,000 whether that comes from your homeowners policy, you, or a combination of both.
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I think most of us understand that you have to have the required amount of liability coverage to properly get coverage under the umbrella policy.