Uniform estimates for the finite-time ruin probability in the dependent renewal risk model

Abstract

This paper investigates the finite-time ruin probability in the dependent renewal risk model, where the claim sizes are independent and identically distributed random variables with strongly subexponential tails, and the interarrival times are negatively dependent. We establish an asymptotic estimate, which holds uniformly for the time horizon varying in the positive half line.

Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi‐Asymptotically Independent or Bivariate Regularly Varying‐Tailed Main Claim and By‐Claim

“…As (2) and (3), define the infinite-time and finite-time ruin probabilities of risk model ( 19) with (⋅) replaced by * (⋅), denoting them by * ( , ) and * ( ), respectively. The following first lemma comes from Corollary of Wang et al [9]; see some similar results in Yang et al [8].…”

“…In the past decade, more and 2 Complexity more attention has been paid to heavy-tailed claims and the dependence between them. In the presence of heavy-tailed claim sizes, Tang [5], Leipus andŠiaulys [6,7], Yang et al [8], Wang et al [9], Liu et al [10], Yang and Yuen [11], Yang et al [12,13], and Chen et al [14] investigated some independent or dependent risk models with no by-claims. Li [15] considered a dependent by-claim risk model with positive interest rate and extendedly varying tailed main claims and by-claims under the pairwise quasi-asymptotical independence structure (see the definition below).…”

On the non-closure under convolution for strong subexponential distributions

“…The properties of class S * and related classes were studied in [6,Sect. 3.4], [8][9][10][11][12][13][14], [18][19][20], and other papers. In particular, it is well known that, under µ F < ∞, it holds that S * ⊂ S ⊂ L .…”

“…showing the validity of (19). It remains to prove inequality (20). Integral from this inequality is bounded from below by J F ,G (x) :=…”

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

“…Leipus and Šiaulys [3] and Kočetova et al [4] considered the claim sizes have strong subexponential distributions and showed the asymptotics of ψ(xt) holds uniformly for t Î[ f (x)¥). Yang et al [5] and Wang et al [6] improved the above results by considering the dependent {θ i i ≥ 1}.…”