Mathematical protocols for decision support in a final context of placing reinsurance futures contracts on the organized financial market.

Summary This work is divided into three parts. The first one presents a strictly financial application . the second one deals with the specific domain of reinsurance . finally the third one studies an example of interaction between these two domains. The first part, specific to the stochastic domain of finance in the context of a complete market, provides explicit expressions for the generalization of the Black-Scholes model to the particular case of the valuation and management of an option on a homographic function of two correlated underlyings that pay dividends. The second part presents the construction and econometric analysis of market price indices for excess catastrophe reinsurance treaties in the United States. Based on a significant data collection, the empirical part covers the period 1975 to 1993. The two types of price indicators provided (one qualitative, the other quantitative) make it possible to set up, in turn, two types of efficiency measurement protocols: that intrinsic to the market, and that of the company's portfolio relative to the market. The third part, specific to stochastic calculus and econometrics, focuses on the organized financial market for natural catastrophe reinsurance futures (traded at the Chicago Board of Trade since 1993). Various proposals for functional optimizations are presented. The idea is to retain a market price index representative of the financial market that allows the introduction of: a family of information tribes converging to a continuous information tribe, and a reference index, in the context of this incomplete market. Finally, we propose, as an example, a valuation and management method in line with the management of a reinsurance portfolio.