Asymptotics for aggregated interdependent multivariate subexponential claims with general investment returns

TL;DR

This paper derives asymptotic estimates for the probability of aggregate claims exceeding thresholds in a multivariate risk model, considering complex dependence and investment returns.

Contribution

It extends asymptotic analysis to general dependence structures and claim distributions, including cases beyond multivariate regular variation.

Findings

Asymptotic estimates for entrance probabilities in multivariate risk models.

Results applicable to both finite and infinite time horizons.

New dependence structures introduced for claim vector modeling.

Abstract

This paper investigates asymptotic estimates for the entrance probability of the discounted aggregate claim vector from a multivariate renewal risk model into some rare set. We provide asymptotic results for the entrance probability on both finite and infinite time horizons under various assumptions regarding the stochastic price process of the investment portfolio, the distribution class of claim vectors, and the dependence structure among the claim vectors. We note that the main results extend beyond the class of multivariate regular variation. Furthermore, we introduce two dependence structures to model the dependence among the claim vectors. In particular, our results are new even in one-dimensional subcase.