Tags: catastrophe insurance, reinsurance, pricing, government
More from: Hanyang Wang, Jieyu Lin

The increasing frequency and strength of catastrophes (natural or man-made) not only severely impact victims and countries but also endanger the viability of the insurance and reinsurance industry. Total economic losses from natural catastrophes and man-made disasters are estimated to be $306 billion in 2017, up from $188 billion in 2016 and much more than the annual average of the previous 10 years. Insured losses have dramatically increased as well. During the period 2001-2010, insured losses from weather-related disasters alone averaged $30 billion annually.

Among diversified ways of government intervention, government as reinsurer is widely considered as an adequate method to resolve the uninsurability problem since the government has the capacity to diversify risks over the whole population and to spread past losses to future generations. Additionally, the government could charge a relatively fair premium and simulate primary insurers to provide catastrophe insurance.

This paper discusses pricing of catastrophe reinsurance provided by government. The discussion starts with a brief review of stylized patterns of catastrophe reinsurance by government worldwide. And based on these, we structure a one-region model, consisting n inhabitants, an insurer and a government. Given with the premium of the catastrophe insurance and taxation, inhabitants decide whether to purchase the insurance or not. Then, with given reinsurance treaty from the government, the insurer makes the insurance pricing decision to maximize its profit. Last, the government makes the reinsurance pricing and taxation decision to maximize the total utility of the whole region. Applying the game theory, we derive the solution to the one-region model and provide numerical analysis based on the analytical solutions.

Our article relates to the literature that analyzes the role of government in catastrophe insurance markets. Despite of some criticisms from free market advocators, government intervention is considered necessary in catastrophe insurance market but how should the government intervene is still a debate. Among diversified ways of government intervention discussed by academics, government as reinsurer is the least problematic scheme. Scholars in favor of this schemes propose that government as reinsurers could stimulate primary insurers supply and keep catastrophe insurance affordable. Whereas, there is few modeling framework systematically investigate the role of government among previous researches. Further, some modeling frameworks describe government intervention as taxing policyholders and providing unlimited guarantee, which is a bit far from practice. We consider an important case in reality: how much does government as reinsurer charge from primary insurer? Since some scholars rebut that government charges premiums away from market prices, our research give much more insight into policies.

Our work also relates to studies on reinsurance pricing with economic method. Previous researches incorporate preferences of the decision makers involved (i.e. insurance buyer and insurance seller) in the determination of insurance prices. The eventual premium is generally derived from the economic indifference principles. However, different decision makers interaction with each other thus we discuss reinsurance pricing in a general equilibrium framework and derive the analytical solution for comparative static studies.

With both analytical solutions and numerical studies, we find that (1) the insurer earn positive profit and inhabitants are indifferent with insured and uninsured in the equilibrium. In other words, government intervention could stimulate market solution by providing reinsurance for primary insurer, (2) further given non-proportional reinsurance treaty, risk-based reinsurance premium rate is related to deductible, coverage ratio and ceiling. The more risk borne by the government, the higher reinsurance rate the government will ask the insurer to hand in, with given scale of the nature risk. When the deductible is zero, the non-proportional reinsurance contract transits into a proportional one that the government covers a certain share of the total loss of the insurer with an upper limitation. And the impact of the reinsurance contract, on the optimal reinsurance rate holds. Moreover, with proportional reinsurance, government needs to cover losses no matter how large the scale of the total loss is, sharing the risk with the insurer all the time. While, subtle loss cannot be covered by the non-proportional reinsurance. (3) With given cover ratio and ceiling, premium of the proportional reinsurance is always higher than that of the non-proportional reinsurance. (4) Also, the price is positive with within-region correlation under extreme conditions. As well, the price is positive with the probability for any individual to be a victim. When extreme events happen, higher correlation between habitants’ claims or higher probability that inhabitants claim losses imply larger scale a catastrophe hits. Greater total loss to the insurer increases the percentage of the insurer’s loss that is above the deductible. Thus a larger share of loss needed to be covered by the government, so that the governmental reinsurance is priced higher.

In conclusion, our results show that the catastrophe reinsurance by government could alleviate catastrophe insurance market failure but premium shall be charged based on both associated risk and treaty. Therefore, the introduction of public catastrophe reinsurance contributes to managing catastrophe risk which becomes increasing challenging all over the world.

The complete paper is available at:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3270669 .