Asymptotic ruin probabilities of a two-dimensional renewal risk model with dependent inter-arrival times

Abstract

This article mainly considers the uniform asymptotics for the finite-time ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. In this model, the two claim-number processes are arbitrarily dependent and each of them is generated by widely orthant dependent claim inter-arrival times. Two types of ruin are studied and for each type of ruin, an asymptotic formula for the finite-time ruin probability is established. These formulae possess a certain uniformity feature in the time horizon.

Keywords:

• Two-dimensional renewal risk model
• heavy-tailed distributions
• finite-time ruin probabilities
• uniform asymptotics

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62P05
• Secondary 62E10

Additional information

Funding

Research supported by National Natural Science Foundation of China (No. 11401415), Tian Yuan foundation (No.11426139), Postdoctoral Research Program of Jiangsu Province of China (No. 1402111C), Jiangsu Overseas Research and Training Program for Prominent University Young and Middle-aged Teachers and Presidents and Fund of Nantong Science and Technology Program (No. BK2014030).