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Consider a catastrophe insurance market in which primary insurers purchase excess of loss reinsurance to transfer their higher-layer losses to a reinsurer. We conduct a portfolio risk analysis for the reinsurer. In doing so, we model the losses to the primary insurers by a mixture structure, which effectively integrates three risk factors: common shock, systematic risk, and idiosyncratic risk. Assume that the reinsurer holds an initial capital C n that is in accordance with its market size n. When expanding its business, the reinsurer needs to comply with a certain VaR-based solvency capital requirement, which determines an infimal retention level r n according to the initial capital C n. As our main results, we find the limit of r n as n→∞ and then establish a weak convergence for the reinsurance portfolio loss. The latter result is applied to approximate the distortion risk measures of the reinsurance portfolio loss. In our …