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More importantly, pandemics are correlated risks, so the insurance company is not reducing any risk by insuring against it.

If they did, everyone's insurance rates would go way up after a pandemic in about the same amount as they would have to pay for the pandemic.

As it is, insurance companies are both not insuring against it and also teeing up to massively increase rates [1].

Why only dip once when you can dip twice?

There are lot of types of insurance that exclude pandemics, but health insurers are unlikely to be one of them.