Résumé: This paper presents the bivariate Poisson-new XLindley distribution (BPNXLD), which may be used to represent dependent and over-dispersed countdata. Among the characteristics considered are the correlation coefficient, mean, and variance of the distribution. Acomparison with several Bivariate distributions is included. The goodness of fit of this novel model iscompared with the bivariate Poisson, bivariate negative binomial and bivariate Poisson-Lindley distributions using two data sets from a German Bundesliga season

Résumé: This paper focuses on weighted balanced loss function under the Esscher principle (WBLF) of which we explore the modern practice of credibility theory and we generalize credibility premiums by using the WBLF. We obtain a distribution-free approach under the WBLF and the Esscher premium by using a minimization technique. Also, we discuss the consistency of the credibility premium generated by this distribution-free approach.

Résumé: This paper focuses on the pricing of variance and volatility swaps under Heston model (1993). To this end, we apply this model to the empirical financial data: CAC 40 French Index. More precisely, we make an application example for stock market forecast: CAC 40 French Index to price swap on the volatility using GARCH(1,1) model.