On bivariate credibility estimator with GLM theory

Credibility theory is one of the cornerstones of actuarial science as applied to casualty and property insurance, based on the concept of limiting the estimator of individual premium to the class of estimators that are linear with respect to all observations of the portfolio. This work deals with the bivariate data(number and amounts of claims of the contracts), we give the bivariate credibility estimator using exponential families and GLM theory. Just like in the case of classical credibility model we will obtain a credible solution in the form of a linear combination of the individual estimate and the collective estimate. And we add the proprieties on exact Bayes premium.Publisher's Versio

On Poisson Quasi-Lindley Distribution and its Applications

This paper proposes a recent version of compound Poisson distributions named the Poisson quasi-Lindley (PQL) distribution by compounding Poisson and quasi-Lindley distributions. Some properties of the distributions are given with estimation and some illustrative examples

Around Gamma Lindley Distribution

Some remarks and correction on a new distribution, Gamma Lindley, of which the Lindley distribution is a particular case, are given pertaining to its parameter space

Existence of solutions and stability for impulsive neutral stochastic functional differential equations

In this paper we prove some results on the existence of solutions and the mean square asymptotic stability for a class of impulsive neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a sufficient condition ensuring the asymptotic stability is proved. The assumptions do not impose any restrictions neither on boundedness nor on the differentiability of the delay functions. In particular, the results improve some previous ones in the literature. Finally, an example is exhibited to illustrate the effectiveness of the results.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de AndalucíaEuropean Mathematical Societ

Existence of periodic positive solutions to a nonlinear Lotka-Votlerra competition systems

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka–Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967–2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature

Stability results for neutral stochastic functional differential equations via fixed point methods

In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a necessary and sufficient condition ensuring the asymptotic stability is proved. The assumption does not require neither boundedness or differentiability of the delay functions, nor do they ask for a fixed sign on the coefficient functions. In particular, the results improve some previous ones proved by Guo, Y., Xu, C., & Wu, J. [(2017). Stability analysis of neutral stochastic delay differential equations by a generalisation of Banach’s contraction principle. International Journal of Control, 90, 1555–1560]. Finally, an example is exhibited to illustrate the effectiveness of the proposed results

On composite length-biased exponential-Pareto distribution: Properties, simulation, and application in actuarial science

The composite length-biased exponential-Pareto (CLBEP) distribution is a new composite distribution that is introduced in this article. This model's probability density function, moments, and quantiles, among other statistical characteristics, are determined mathematically. The parameters' maximum-likelihood estimation and stochastic ordering are discussed. A comparison study with other new composite and conventional distributions is also included. Specifically, using two actual fire insurance data sets, the goodness of fit of this new model is contrasted with the composite exponential-Pareto, composite lognormal-Pareto, and composite Rayleigh-Pareto distributions (Algerian and Danish fire insurance losses).2010 AMS subject classifications62E10; 60E05

On Volatility Swaps for Stock Market Forecast: Application Example CAC 40 French Index

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

Asymptotic Behavior of Some Parabolic Equations and Application in Image Restoration

In this paper, we consider some nonlinear parabolic problem involving the well known p-laplacian and some operator having exponential growth with respect to the gradient. We start by dealing the asymptotic behavior for some evolution equation then we give some numerical results with an application in image processing