Optimal Reinsurance Contract With The Mix Use Of Indexed Catastrophe Bond

Insurance-linked securities, emerging at the beginning of 1990s, are shown as an important financial innovation that shifting catastrophe risk from insurance markets to financial markets. In this paper, we aim to analyze the interaction between reinsurance and Indexed Catastrophe Bonds (ICB ), the main kind of insurance-linked securities, in catastrophe risk management.A major problem for insuring catastrophe risk is that, as a catastrophe event happens, the reinsurance contracts are often subject to default risk, meanwhile, which the primary insurer and reinsurer have divergent beliefs about the probability distribution of due to information asymmetry. On the other hand, the indexed catastrophe bonds can be designed to completely avoid default risk. However, the payout from catastrophe bonds are tied to some stochastic variable, such as market loss index or parametric triggers, which is correlated, but not identical, with the insured's actual losses. Therefore, it will usually not provide a perfect hedge, there will be some mismatch, the so-called basis risk.The purpose of this paper is to investigate how the divergent beliefs of total default risk and the availability of coverage generated through CAT bonds affect the structure of an optimal reinsurance contract when (re)insurance and CAT bonds are used simultaneously.For this purpose, we analyze the optimal risk-management mix in an expected utility model. It shows that:(1) The availability of coverage generated through CAT bonds affect the optimal risk-management mix, ICB is substitute for reinsurance in some degree.(2) Divergent beliefs of default risk affect the structure of the optimal reinsurance. The optimal deductible is positive if and only if the subjective probability of performance estimated by the primary insurer is lower than reinsurer under an actuarially fair reinsurance contract; Whether the optimal marginal reinsurance indemnity above deductible is equal to or smaller than one, is affected both by the insurer's and reinsurer's divergent belief of hazard rate and by the basis risk of Cat bonds;(3) The existence of a none-zero deductible in the mix of catastrophe risk management would not be affected by the availability of coverage generated through CAT bonds, but would be affected by the divergent beliefs of default risk, or by the unfair premium condition.(4) Finally, we investigate how design of the trigger condition and divergent assessment of default risk affects the interaction between the optimal reinsurance and indexed CAT bonds.The main innovation of this paper is to investigate how the optimal reinsurance in the optimal risk-management mix is affected by both the divergent beliefs of total default risk and the design of trigger condition of indexed catastrophe bonds, and how a non-zero deductible is decided when both reinsurance and CAT bonds are used simultaneously.The conclusion is enriching the demand theory of the insurance-linked securitization in study. On the other hand, as an application of our conclusion, strengthening the construction of rating system and CAT models to eliminate the divergent beliefs of default risk, can be useful for the development of the insurance-linked securities. Meanwhile, it can be helpful for China to find another available tool, shifting large loss events, such as earthquake and flood, from insurance markets to financial markets, to manage these catastrophe risks.