# 1 Introduction

Over the last 50 years, insured losses caused by natural disasters have followed an increasing trend.<sup>1</sup> Population increase and economic growth on the one hand, the development of insurance markets on the other hand, have expanded the global insurance industry. In the future, continued growth and development in at-risk zones and possible changes in climate are likely to maintain or amplify this trend. This evolution would represent a signicant challenge for the insurance industry (Herweijer et al., 2009). Reinsurance rms are particularly exposed to these issues as they supply disaster coverage to insurance companies for hurricanes, windstorms or earthquakes, among others.

The reinsurance market resilience is a concern for the insurance sector. In particular, insurers need to assess the ability of the reinsurance sector to absorb large shocks. More specically, they need to know how important losses impact the reinsurance market capacity, reinsurance prices and the time needed for the sector to recover.<sup>2</sup> From a public policy perspective, one may ask if a modied solvency regulation increases the system resilience, and how it impacts the market. Resilience is a key issue in the nance industry in general. It has been raised again following the nancial crisis, as the ability of the nancial markets to withstand shocks has been questioned. The economic literature has examined the question of regulations for nancial industries and especially insurance industry (see Plantin and Rochet (2007) for a review). Our study focuses on the specic case of the robustness of the reinsurance market to large shocks but its conclusions are of interest for the nancial sector in general.

In this paper, we analyze the impact of important catastrophic losses on the reinsurance market, using a dynamic model of the reinsurance sector based on a solvency constraint for reinsurance rms. We thus enrich Winter (1994) rst dynamic model of the competitive insurance market. This solvency constraint is represented by a bounded probability of default, and the model is related to the classical capacity constraint hypothesis. Furthermore, we take into account the strategic eects of rms individual behavior on the market equilibrium, completing the traditional competitive view of the insurance industry (Hardelin and Lemoyne de Forges, 2009).

Model results show a market dynamics that reproduces many real-world observations, suggesting that the capacity-constraint hypothesis is able to explain the observed variability in reinsurance prices and quantities, provided that strategic behavior is taken into account. We nd path-dependency, i.e. the fact that the consequence of a one shock depends on previous years losses and reinsurers response. We characterize and quantify the resilience of the sector through the time necessary to restore reinsurance capacity after large disasters. We provide a sensitivity analysis of the key parameters including higher loss levels and series of losses. We show that improving the ability of the reinsurance market to cope with large losses and reducing reinsurer default probability that is consolidating reinsurance rms with regard to risk has a cost, due to its negative impact on market prices and capacity. Thus we exhibit a regulation trade-o between market resilience and eciency.

The paper is organized as follows: Section 2 briey describes the main characteristics of the reinsurance market for natural catastrophe risks. Section 3 presents the underlying economic

> 1See Munich Re's long-term statistics: http://www.munichre.com/en/ts/geo\_risks/ natcatservice/long-term\_statistics\_since\_1950/default.aspx

> 2Capacity refers to the term used by Cummins et al. (2002) and dened as follows: For any losses for which the reinsurance companies are liable, the capacity of the reinsurance market is the proportion of the liabilities that is deliverable to their customers, given the nancial resources of the companies, and all their risk management arrangements (retrocession, catastrophe bonds).

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