New examples of heavy-tailed O-subexponential distributions and related closure properties

Lin, Jianxi; Wang, Yuebao

doi:10.1016/j.spl.2011.12.011

Cited by 26 publications

(13 citation statements)

References 9 publications

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“…Next, we prove Proposition 12(b). The proof is analogous to the proof of the same assertion for the class OS, see [17], Lemma 3.1. Let L i := X i ∧ Y i for i ∈ {1, 2}.…”

Section: Proof Of Proposition 12mentioning

confidence: 75%

A new class of large claim size distributions: Definition, properties, and ruin theory

Beck¹,

Blath²,

Scheutzow³

2015

Bernoulli

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We investigate a new natural class J of probability distributions modeling large claim sizes, motivated by the 'principle of one big jump'. Though significantly more general than the (sub-)class of subexponential distributions S, many important and desirable structural properties can still be derived. We establish relations to many other important large claim distribution classes (such as D, S, L, K, OS and OL), discuss the stability of J under tail-equivalence, convolution, convolution roots, random sums and mixture, and then apply these results to derive a partial analogue of the famous Pakes-Veraverbeke-Embrechts theorem from ruin theory for J . Finally, we discuss the (weak) tail-equivalence of infinitely-divisible distributions in J with their Lévy measure.

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“…Next, we prove Proposition 12(b). The proof is analogous to the proof of the same assertion for the class OS, see [17], Lemma 3.1. Let L i := X i ∧ Y i for i ∈ {1, 2}.…”

Section: Proof Of Proposition 12mentioning

confidence: 75%

A new class of large claim size distributions: Definition, properties, and ruin theory

Beck¹,

Blath²,

Scheutzow³

2015

Bernoulli

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“…It is worth mentioning that the inclusion S(γ ) ⊂ L(γ ) ∩ OS is strict, as shown by examples in Klüppelberg and Villasenor (1991) for γ > 0, and in Leslie (1989) for γ = 0. More recently, Lin and Wang (2012) have constructed some new distributions belonging to L ∩ OS but not to S. Thus the distribution class L(γ ) ∩ OS \ S(γ ) appears to be a large one meriting further investigation. On the other hand, it also should be noted that Theorem 1.3 still delivers only a sufficient condition.…”

Section: Remark 12mentioning

confidence: 99%

“…More works on the class OS may be found in Cheng and Wang (2012), Klüppelberg and Villasenor (1991), Lin and Wang (2012), Watanabe and Yamamura (2010), Yu and Wang (submitted for publication), and so on.…”

mentioning

confidence: 99%

Some properties of the exponential distribution class with applications to risk theory

Cheng

Fenglian

Pakes

et al. 2012

Journal of the Korean Statistical Society

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“…In practice, many distributions are not convolution equivalent. Even in the common exponential distribution class, which contains the convolution equivalent distribution class, there are many such distributions, we refer to Pitman (1979), Embrechts and Goldie (1980), Murphree (1989), Leslie (1989), Lin and Wang (2012), Wang et al (2016), among others. In the present paper, we also provide some examples.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of convolution with the semi-regular-variation tail and its application to risk

et al. 2018

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In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the semi-regular-variation-tailed distribution class. In the new class, although all distributions are not convolution equivalent, there still have some good properties.We give the precise tail asymptotic expression of convolutions of these distributions, and prove that the class is closed under convolution. In addition, we do not need to require the corresponding random variables to be identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, thus obtain the precise asymptotic estimation of the finite time ruin probability.

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New examples of heavy-tailed O-subexponential distributions and related closure properties

Cited by 26 publications

References 9 publications

A new class of large claim size distributions: Definition, properties, and ruin theory

A new class of large claim size distributions: Definition, properties, and ruin theory

Some properties of the exponential distribution class with applications to risk theory

Asymptotics of convolution with the semi-regular-variation tail and its application to risk

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