International Journal of Statistics and Probability; Vol. 5, No. 2; 2016 ISSN 1927-7032 E-ISSN 1927-7040 Published by Canadian Center of Science and Education 100 Mixed Method of Extreme Value Theory, with Application to the Calculation of the Portion of Each Claim Payable by the Reinsurer of Excess of Sinister Yingmei Xu 1 , Kane Ladji 2 & Diawara Daouda 3 1,3 Zhongnan University of Economics and Law, Wuhan China 2 Faculty of Economics and Management FSEG Bamako, Mali Correspondence: Diawara Daouda, Ph.D Candidate Zhongnan University of Economics and Law, Wuhan China. Tel: 86-132-6472-1138. E-mail : btddiawara@yahoo.fr Received: January 26, 2016 Accepted: February 10, 2016 Online Published: February 25, 2016 doi:10.5539/ijsp.v5n2p100 URL: http://dx.doi.org/10.5539/ijsp.v5n2p100 Abstract In the literature many determinists approaches (numerical and graphical methods), probability (the probability law, extreme value theory, Bayesian methods) exist for the detection of grave sinister. In this paper, we will give a new characterization of the mixed method of extreme value theory. These results are applied to the simulated data of a Malian insurance company. Keywords :insurance, claims management, minimizing the variance, convex combination of two and three thresholds 2000 Mathematics Subject Classification: 60G52, 60G70, 62G20, 62G32 1. Introduction Insurance is a transaction whereby a person undertakes to indemnify another person, the insured in case of occurrence of a specified risk, against the prior payment of a premium or a contribution. Insurance occupies a very important place in the modern economy: its mechanism helps increase the level of protection of all individuals, and practice has been made mandatory in many areas. The insurance mechanism is based on risk compensation if all policyholders are subject to risk, the likelihood that it will achieve for all insured is low. The victims are compensated thanks to contributions from the community of contributors. The insurer must be able to predict the loads of sinister it will have to bear because of the risks it covers when establishing its insurance policies. These evaluations are of great importance for the insurance company to avoid ruin and insurance solvency of its portfolio. So predict the occurrence of such expenses sinister is very important to take precautions. Usually these assessments are conducted by the insurer and the reinsurer. Reinsurance, Insurance whereby an insurer is guaranteed by another company own risk. The extreme value theory allows, in fact, establish the scenarios of the calculation of the portion of each sinister to load of the excess of loss reinsurer, allowing the insurance company to consider these sinister surpluses and keep its solvency. Reinsurance excess of loss covers the portion of each individual claim excess a given priority, limited to a capacity granted by the reinsurer. We place ourselves in the collective risk model. Let N be the number of sinister and N X X X ,..., , 2 1 the realizations of X, which is the random variable representing the amounts of loss. As usual we assume mutual independence of random variables. Let then D priority referred to above. Let then D priority referred to above, or deductible, cover and let C (capacity) offered by the reinsurer. Then, the portion of each sinister i X N i ,..., 1  is dependent reinsurer min( , max(0, )) i i R C X D   (1) 2. Mixed Method of Extreme Value Theory We assume that the extreme value theory is known. This new method was proposed in ( Noureddine and al., 2009) to determine a threshold, at which a unit is declared atypical minimizing the variance of a convex combination of thresholds obtained by the mean excess function and generalized Pareto distribution (extreme quantile were estimated with a probability of 99, 9% being an extreme value for the distribution of amounts of sinister with a confidence level of 95%). 1 U be the threshold beyond which a unit is declared as extreme, obtained by the mean excess function and 2 U the threshold beyond which a unit is declared as extreme, obtained by the GPD function.