A uniform asymptotic estimate for discounted aggregate claims with subexponential tails

Hao, Xuemiao; Tang, Qihe

doi:10.1016/j.insmatheco.2008.03.009

Cited by 78 publications

(40 citation statements)

References 17 publications

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“…We establish local uniformity for the obtained asymptotic formulae for the subexponential case and global uniformity for the extended regularly varying case. More importantly, in comparison with the corresponding existing results of Tang (2007) and Hao and Tang (2008) in the case of independent X and θ, our formulae successfully capture the impact of the dependence structure of (X, θ ).…”

Section: J LI Et Alsupporting

confidence: 57%

“…Hence, Theorem 2.1 of Hao and Tang (2008) corresponds to our Theorem 2.1 for the case of independent X and θ. The expression ofλ t given in (2.8) for the general case of dependent X and θ shows that our results successfully capture the impact of the dependence structure of (X, θ ) on the tail behavior of the discounted aggregate claims.…”

Section: Theorem 22 Consider the Discounted Aggregate Claims Descrimentioning

confidence: 65%

“…Following the proof of Lemma 4.2 of Hao and Tang (2008) By the arbitrariness of δ in (5.8) and (5.10), we prove the uniformity of (2.7) for t ∈ (T 0 , ∞].…”

Section: Proof Of Theorem 22mentioning

confidence: 98%

“…We follow the proof of Theorem 2.1 of Hao and Tang (2008), but we need to overcome some technical difficulties due to the dependence structure of (X, θ ).…”

Section: Proof Of Theorem 21mentioning

confidence: 99%

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Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Tang

2010

Adv. Appl. Probab.

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Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

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Section: J LI Et Alsupporting

confidence: 57%

Section: Theorem 22 Consider the Discounted Aggregate Claims Descrimentioning

confidence: 65%

“…Following the proof of Lemma 4.2 of Hao and Tang (2008) By the arbitrariness of δ in (5.8) and (5.10), we prove the uniformity of (2.7) for t ∈ (T 0 , ∞].…”

Section: Proof Of Theorem 22mentioning

confidence: 98%

“…We follow the proof of Theorem 2.1 of Hao and Tang (2008), but we need to overcome some technical difficulties due to the dependence structure of (X, θ ).…”

Section: Proof Of Theorem 21mentioning

confidence: 99%

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Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Tang

2010

Adv. Appl. Probab.

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“…It is well known that the following proper inclusion relationship should hold for the distribution of heavy-tail: Embrechts et al (1997;Kluppelberg and Stadtmuller, 1998;Tang and Tsitsiashvili, 2003;Li et al, 2009;Hao and Tang, 2008) From the study of many contexts and literatures, we easily found that the renewal risk model with constant interest rate mainly involves the independent structure between the claim sizes and arrival times of successive claims; this limits the usefulness of the obtained results to some extent. However, the introduction of dependent structure to risk models has captured more and more researchers' attention in recent years and it provides a special perspective for the ruin probabilities theory.…”

Section: Jmssmentioning

confidence: 99%

Asymptotic Behavior of Finite-Time Ruin Probability in a by-Claim Risk Model With Constant Interest Rate

Wang¹

2014

Journal of Mathematics and Statistics

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This study investigates the ruin probability of a renewal risk model with constant interest rate and by-claim parts. We assume that the claim size and the inter-arrival time satisfy a certain dependent structure with some additional assumptions on their distribution functions. In particular, we study the asymptotic behavior of P(R * δ (t, x) >x), which holds uniformly in a finite interval. In this way, we significantly extend the Li's result regarding the pairwise strong quasi-asymptotically independent random variables.

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

Guo

Wang

2012

Appl Stoch Models Bus & Ind

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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.

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A uniform asymptotic estimate for discounted aggregate claims with subexponential tails

Cited by 78 publications

References 17 publications

Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Asymptotic Behavior of Finite-Time Ruin Probability in a by-Claim Risk Model With Constant Interest Rate

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

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