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Asymptotics for Bivariate Risk Models with Random-Size Clusters of Dependent Claims
Abstract
This paper investigates finite-horizon tail and ruin asymptotics for models with random-size clusters of dependent main and delayed claims under Levy investments. Under long-tailed, dominatedly varying claim distributions, a conditional, uniformly weighted Ko-Tang condition within clusters, and moment conditions, univariate asymptotics are derived for discounted aggregate claims and ruin probabilities. For two business lines sharing renewal arrivals but having independent claim marks and Levy processes, marginal and joint tail asymptotics are established as thresholds diverge, without restricting their ratio. Results provide asymptotic formulas for ruin in both lines, simultaneous ruin, and ruin in at least one line.
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BibTeX
@misc{lu2026asymptotics,
title = {{Asymptotics for Bivariate Risk Models with Random-Size Clusters of Dependent Claims}},
author = {Dawei Lu and Yiqing Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11256},
eprint = {2609.11256},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11256},
}
RIS
TY - UNPB
TI - Asymptotics for Bivariate Risk Models with Random-Size Clusters of Dependent Claims
AU - Dawei Lu
AU - Yiqing Chen
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.11256
UR - https://arxiv.org/abs/2609.11256
AB - This paper investigates finite-horizon tail and ruin asymptotics for models with random-size clusters of dependent main and delayed claims under Levy investments. Under long-tailed, dominatedly varying claim distributions, a conditional, uniformly weighted Ko-Tang condition within clusters, and moment conditions, univariate asymptotics are derived for discounted aggregate claims and ruin probabilities. For two business lines sharing renewal arrivals but having independent claim marks and Levy processes, marginal and joint tail asymptotics are established as thresholds diverge, without restricting their ratio. Results provide asymptotic formulas for ruin in both lines, simultaneous ruin, and ruin in at least one line.
ER -