[delecti]

Can you explain that logic?

The possible cases I can see are: the insurance prices are reasonably fair (roughly equal to risk percent times insured value, plus some profit buffer), or they're significantly higher or lower than that "fair" amount. Given that, I have trouble seeing a case where the rational action is insuring part of the value. If the cost is significantly higher than the risk-adjusted value, then it wouldn't make sense to insure at all, and if it's roughly equal or significantly lower then it would make sense to insure as much as possible.

[octodog]

It's no different to choosing your level of cover on life insurance or your level of excess on car insurance. Different companies and circumstances will have different risk profiles and will therefore require different levels of insurance.

[delecti]

I'm not sure any of those are the same though. Everyone dies exactly once, and you can plausibly never need to invoke your car insurance, but a business shipping large amounts of good will surely incur some stochastic but average-able level of loss.