Ruin Probabilities for a Multidimensional Risk Model With Non-Stationary Arrivals and Subexponential Claims

Abstract

Consider a multidimensional risk model, in which an insurer simultaneously confronts m (m ≥ 2) types of claims sharing a common non-stationary and non-renewal arrival process. Assuming that the claims arrival process satisfies a large deviation principle and the claim-size distributions are heavy-tailed, asymptotic estimates for two common types of ruin probabilities for this multidimensional risk model are obtained. As applications, we give two examples of the non-stationary point process: a Hawkes process and a Cox process with shot noise intensity, and asymptotic ruin probabilities are obtained for these two examples.

Uniform Asymptotics for Finite-Time Ruin Probabilities of Risk Models with Non-Stationary Arrivals and Strongly Subexponential Claim Sizes

“…Recently, Refs. [10,11] considered the claim-number processes may not be stationary and ergodic and satisfy the large deviations principle (LDP for short). A family of probability measures {μ t } t Î(0¥) on a Hausdorff topological space (MF M ) satisfies the LDP with rate function I: M ®[0¥), if I is a lower semi-continuous function and the following inequalities hold for every Borel set B:…”

Precise large deviations for a multidimensional risk model with regression dependence structure

“…It is well known that, with the increasing diversification of insurance companies' business types, the multidimensional risk model can reflect the influence of different businesses on insurance companies' solvency more comprehensively. Therefore, the risk theory analysis of multidimensional risk model has attracted the attention of some researchers; see, for example, see, Chen et al [5], Loukissas [12], Fu and Liu [8], Lu [13], Shen et al [15], Wang and Wang [19] and references therein.…”

On some effects of dependencies on an insurer’s risk exposure, probability of ruin, and optimal premium loading

“…This is just for the sake of simplicity and readability, since all theoretical results can be readily extended to any number of risks, though numerical computations may become exceedingly laborious. Second, the class of processes considered in this paper includes a broad range of dependencies between risks, but it does not include processes where dependencies are due to some form of joint modulation of the claim numbers intensities, like in Cox processes [2,12,16,24,27], or in Hawkes processes [12,24,28]. We will address some of these later classes in a forthcoming paper.…”