Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Two-Dimensional Continuous Model in Bimolecular Reactive Transport

In this work, a continuum 2D model is proposed to study the interaction at the interface of reactive transport processes in porous media. The analysis of the segregation produced by poor reactant homogenization at the poral scale is addressed by a parametric heuristic model that considers the relative gradient of the reacting species involved in the process. The micro inhomogeneities are incorporated by means of longitudinal and transversal mechanical dispersion coefficients. A two-dimensional continuous model for the bimolecular reactive transport is considered where modelling parameters are estimated numerically from experimental data. A competitive effect between segregation and dispersion is observed that is analyzed by means of numerical experiments. The two-dimensional model reproduces properly both the total mass of the product as well as its increase with the velocity of flow and the inhomogeneity of the advanced front. The methodology used is simple and fast, and the numerical results presented here indicate its effectiveness.