Moderate deviations for multidimensional aggregate claims with arbitrary dependence between claim sizes and waiting times

Abstract

Consider a multidimensional renewal risk model, in which the claim sizes ${\mathit{X}}_k,k\ge 1,$ form a sequence of independent and identically distributed random vectors with non negative components allowed to be dependent on each other, and the inter-arrival times form a sequence of p-extended negatively dependent random variables. By allowing arbitrary dependence between claim sizes and waiting times, we obtain the moderate deviations for the multidimensional aggregate claims with consistently varying tails.

Keywords:

• Moderate deviation
• multidimensional risk model
• p-extended negatively dependent
• consistently varying distributions

Mathematics Subject Classification 2020:

• Primary: 60F10
• 91B05
• Secondary: 60G50
• 62H99

Acknowledgments

All the authors are grateful to the two anonymous referees for their constructive comments and suggestions that make the paper significantly improved in both the content and presentation.

Disclosure statement

No potential conflict of interest was reported by the author(s).