Asymptotics for the ruin probabilities of a two‐dimensional renewal risk model with heavy‐tailed claims

In this paper, we consider two dependent classes of insurance business with heavy‐tailed claims. The dependence comes from the assumption that claim arrivals of the two classes are governed by a common renewal counting process. We study two types of ruin in the two‐dimensional framework. For each type of ruin, we establish an asymptotic formula for the finite‐time ruin probability. These formulae possess a certain uniformity feature in the time horizon. Copyright © 2010 John Wiley & Sons, Ltd.     

Uniform asymptotic estimates for ruin probabilities of renewal risk models with exponential Lévy process investment returns and dependent claims

This paper investigates the ruin probabilities of a renewal risk model with stochastic investment returns and dependent claim sizes. The investment is described as a portfolio of one risk‐free asset and one risky asset whose price process is an exponential Lévy process. The claim sizes are assumed to follow a one‐sided linear process with independent and identically distributed step sizes. When the step‐size distribution is heavy tailed, we establish some uniform asymptotic estimates for the ruin probabilities of this renewal risk model. Copyright © 2012 John Wiley & Sons, Ltd.