# The uniform local asymptotics of the total net loss process in a new time-dependent bidimensional renewal model

## TL;DR

This paper analyzes the asymptotic behavior of the total net loss process in a bidimensional renewal risk model with time-dependent dependence, providing new examples of local subexponential distributions and their properties.

## Contribution

It introduces a new time-dependence structure in a bidimensional renewal risk model and derives uniform local asymptotics for the total net loss process.

## Key findings

- Derived uniform local asymptotics for the total net loss process.
- Provided examples of joint distributions satisfying the dependence conditions.
- Identified a local subexponential distribution with non-almost decreased local distribution.

## Abstract

In this paper, we consider a bidimensional renewal risk model with constant force of interest, in which the claim size vector with certain local subexponential marginal distribution and its inter-arrival time are subject to a new time-dependence structure. We obtain the uniform local asymptotics of the total net loss process in the model. Moreover, some specific examples of the joint distribution satisfying the conditions of the dependence structure are given. Finally, in order to illustrate a condition of the above result, a local subexponential distribution is find for the first time that, its local distribution is not almost decreased.