Regarding Richard Tol's comment as included below, interagency discussions over the draft IPCC chapter that contained a discussion of these matters suggests that the situation is somewhat more complex and cannot be so easily dismissed. While one would think that the insurance industry could wily-nilly change their rates to adjust, in reality they are considerably less flexible due to political choices and restrictions. Thus, in the US many states control rates, or require all areas to be covered, or rates to be the same even where risks are not. All of these decisions, and more, are based on choices made to reflect social values, etc. As it turns out, insurance companies are backed up by reinsurance companies.
Insurance companies try to offer the lowest rates and then depend on their reinsurance.
This is tending to cause problems with the reinsurance agencies, and what they need is information on the changing variability so they can impose proper rates on the insurance companies. Another component of the matter is the character of the investments that back up the insurance industry, and how fluid and safe and subject to climate change they are. Much of the investment turns out to be in structures and land developments that have long lifetimes, so cannot move if they then become vulnerable to new or greater climatic fluctuations. For financial security, these investments should not be in the same areas where they are insuring so they are not subject to same event risks. The insurance industry is also, however, sensitive to shifts and changes well before we can attribute the changes with certainty.