This paper presents a dynamic model of the reinsurance market for catastrophe risks. The model is based on the classical capacity-constraint assumption. Reinsurers choose every year the quantity of risk they cover and the level of external capital they raise to cover these risks. The model exhibits time dependency and reproduces a market dynamics that shares many features with the real market. In particular, market price increases and reinsurance coverage decreases after large shocks, and a series of smaller losses may have a deeper impact than one larger loss. There is a significant oligopoly effect reducing reinsurance supply, and the market is segregated into strategic large actors that influence market prices and price-taker smaller firms. A regulation trade-off between market efficiency and resilience is identified and quantified: improving the ability of the market to cope with exceptional events increases the cost of reinsurance. This model provides an interesting basis to analyze further capacity needs for the insurance industry in view of growing worldwide exposure to catastrophic risks and climate change.