We study how traditional reinsurance and CAT bonds can be combined to build an optimal catastrophe insurance programme …. We develop a contingent claims model to investigate the imperfections and limitations of the reinsurance market stemming … for reinsurance contracts that cover the higher and less probable layers of losses. We show that the optimal hedging …

distribution.We provide a characterization of optimal reinsurance indemnities, and we show that they are ofa layer-insurance type …, the optimal reinsurance indemnitiesenable us to identify a representative reinsurer in both situations. Finally, two …

downside risk measures (value-at-risk, expected shortfall) or reinsurance premiums and related quantities (large claim index … for various measures and indices, and finally provide applications on insurance losses and financial risks. …