rms relay on it, and the less the market correction on prices. This leads to a higher capacity of the reinsurance market to supply coverage after important losses when cost of external capital is low. This impact is only visible during tight markets.

- Impact of initial capital ( _Wr_<sup>0):Inthepresentcasewithaperfectlysymmetricmarketwithno</sup> entry nor exit, all reinsurers have an optimal capital target that they all tend to reach. A dierence in initial capital disappears after periods of soft market during which the reinsurers can replenish their capital.

- Impact of the number of reinsurers ( _Nr_ ): When we distribute the same total capital among dierent numbers of reinsurers, the oligopoly eect is quite clear: the fewer the reinsurers, the lower market capacity and the higher the prices during soft markets. There is therefore a clear gain from increased competition in the market. However, impact of important losses lead to the same depletion of capacity.

- Impacts of the solvency constraint ( _πlim_ ): Results show that the lower the solvency constraint, i.e. the higher _πlim_ , the higher the capacity of the reinsurance market in soft market and the higher the time needed for recovery after an important loss. However, as path dependency is important, a rened analysis of the impact of this constraint, particularly on the resistance to high shocks, is conducted in Section 7.

- Impacts of the limit share of buy backs ( _κ_ ): The sensitivity analysis shows that market capitalization stays higher over the scenario when _κ_ is small, as rms can not buy back as many shares as they would for higher level of _κ_ . Consequently, market resilience to large losses is higher.

# 6 Asymmetric market and reinsurer bankruptcy

## 6.1 Market segmentation between two sizes of reinsurers

To investigate a more realistic market, we build a ctive reinsurance market from available market data. The reinsurance market is characterized by a certain concentration that has increased in the last decade. The current market involves big reinsurance rms such as Swiss Re and Munich Re, smaller reinsurers, and new reinsurers as the Bermudian. However, as reinsurance companies oer coverage on several markets (life, disasters...), we do not have specic data on the capital linked to disaster risks and on the market shares on the natural-disaster market. We use as a proxy the market shares as obtained from Standard and Poor's (2008) on the reinsurance market for all lines of risk: in 2007, the four biggest reinsurance companies accounted for 48 % of the market. We consider a market with 4 large reinsurers that each have an initial wealth _W_ 0 of $ 22 _._ 5 bn, and 10 small reinsurers that have an initial wealth of $ 3 bn. This market is still ctive, but it is consistent with the type of concentration observed in the industry. The Geneva Association Systemic Risk Working Group (2010) presents a concentration curve for the reinsurance market where the 10 biggest reinsurers share 80% of the market and the ve biggest more than 50% in 2008. The market parameters used are the same than in the reference reinsurance-market simulation. Figure 6 presents the results of this simulation. The smaller reinsurance companies are represented in solid gray and the larger ones in dashed gray. The interpretation of the output graphs is essentially the same as in the reference simulation. However, several interesting features appear due to the 16