Consider a catastrophe insurance market in which primary insurers purchase reinsurance to transfer their higher-layer risks to the reinsurer. When expanding its business, if the reinsurer does not hold enough initial risk reserve that is commensurate with its business scale, it has to raise the retention level to fulfill the solvency capital requirement. In this work, we conduct an extreme risk analysis for this reinsurance business. In doing so, we assume that the losses to the primary insurers are subject to idiosyncratic risk, systematic risk, and common shock, and we model the insurance losses by a mixture structure which effectively integrates the three risk sources together. Our main results are precise asymptotic formulas for the tail probability of the reinsurance portfolio losses under either a regularly varying systematic risk or a regularly varying common shock, showing that the reinsurance portfolio losses are dominated by whichever one of the systematic risk and the common shock has a heavier tail. Intensive numerical studies are implemented to illustrate how environmental changes in the insurance market affect the reinsurance portfolio losses.