Asymptotics for a nonstandard risk model with multivariate subexponential claims and constant interest force

TL;DR

This paper investigates the asymptotic behavior of the entrance probability for discounted aggregate claims in a multivariate risk model with subexponential claims, considering both finite and infinite time horizons and incorporating dependence structures.

Contribution

It introduces new asymptotic results for multivariate subexponential claim models with dependence, extending classical risk theory to more complex, realistic scenarios.

Findings

Derived asymptotic formulas for finite and infinite horizons

Specialized results for multivariate regularly varying claims

Applied findings to ruin probability analysis with Brownian perturbations

Abstract

In this paper, the asymptotic behavior of the entrance probability of discounted aggregate claims of a certain family of rare sets is studied, considering the finite and infinite time horizons. This multivariate risk model, driven by a common counting process, has a constant interest rate and allows the interdependence of claim vectors. For the finite time horizon, the multivariate subexponential distribution of the common claim vector and the weak dependence structure of regression dependence are used. For the infinite time horizon, the claim vector is taken from a smaller distribution class, and the weak dependence structure is more general. Both results are derived under some additional assumptions on the moments of the counting process, which is fulfilled by all inhomogeneous renewal processes and many quasi-renewal processes, respectively. Moreover, the results are specialized to the multivariate regularly varying case, where more explicit results on the asymptotic behavior of the entrance probability of the discounted aggregate claims are derived. At the end of the paper, the results obtained are used to study the finite and infinite time horizon ruin problems of a risk model with eventual Brownian perturbations.