Asymptotic Estimates for the Ruin Probability of a Multidimensional Delay-Claim Risk Model with Dependent Claims

This paper studies a multidimensional delay-claim risk model in which an insurance company operates $d (d≥2)$ lines of business exposed to a common renewal counting process. Each catastrophic event simultaneously produces main and delayed claims across all business lines, where the delayed claims are settled after random delay periods. The surplus process incorporates a geometric Lévy price process to describe investment returns. Assuming that the main and delayed claims follow subexponential distributions and satisfy a conditional linear dependence structure, we derive asymptotic estimates for the finite-time ruin probability. The obtained results extend existing findings on delay-claim models to the multidimensional framework and contribute to a deeper understanding of ruin behavior under dependence and heavy-tailed risks.