We probably disagree on definitions, because the term risk can sometimes refer to the expected damage and sometimes to the variance of the damage. So I will try

We probably disagree on definitions, because the term risk can sometimes refer to the expected damage and sometimes to the variance of the damage. So I will try to express myself more clearly: Let's say you have a house worth $100,000 and statistically it burns down once in 1000 years. This means that the expected damage is $100 per year, but the variance is very high because once the house burns down, the damage is 1000 times greater than the expected damage. With insurance, however, the variance is zero because you pay the same amount every year, whether your house burns down that year or not. I would argue that with a perfect insurance you would only pay the expected loss, i.e. $100 per year, and not more or less, because ideally the insurance has accurately assessed the expected loss and diversified the variance away. However, with less ideal risk assessment, you could pay more or less because other houses burn more or less often.