Randomly weighted sums of subexponential random variables with application to capital allocation

Tang, Qihe; Yuan, Zhongyi

doi:10.1007/s10687-014-0191-z

Cited by 76 publications

(36 citation statements)

References 30 publications

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“…Θ i , then the investigation on P(S n > x), P(M n > x) and P(M ∞ > x) boils down to the study of the asymptotics for the tail probabilities of randomly weighted sums and their maximum. In the presence of subexponential insurance risks, [16] established the asymptotic formula…”

Section: 3)mentioning

confidence: 99%

Asymptotics for a discrete-time risk model with Gamma-like insurance risks

Yang

Yuen²

2015

Scandinavian Actuarial Journal

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Consider a discrete-time insurance risk model with insurance and financial risks. Within period i, the net insurance loss is denoted by X i and the stochastic discount factor over the same time period is denoted by Y i. Assume that {X i , i ≥ 1} form a sequence of independent and identically distributed real-valued random variables with common distribution F ; {Y i , i ≥ 1} are another sequence of independent and identically distributed positive random variables with common distribution G; and the two sequences are mutually independent. Under the assumptions that F is Gamma-like tailed and G has a finite upper endpoint, we derive some precise formulas for the tail probability of the present value of aggregate net losses and the finite-time and infinite-time ruin probabilities. As an extension, a dependent risk model is considered, where each random pair of the net loss and the discount factor follows a bivariate Sarmanov distribution.

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Section: 3)mentioning

confidence: 99%

Asymptotics for a discrete-time risk model with Gamma-like insurance risks

Yang

Yuen²

2015

Scandinavian Actuarial Journal

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“…This section recalls two important lemmas regarding the tail probabilities of sums of randomly weighted subexponential random variables. The following first lemma is a restatement of Theorem 1 of Tang and Yuan (2014): Lemma 1. Let X 1 , .…”

Section: Lemmasmentioning

confidence: 99%

A Renewal Shot Noise Process with Subexponential Shot Marks

Chen

2019

Risks

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“…The following lemma considers the tail behavior of the randomly weighted sums with heavy-tailed primary r.v.s, which comes from [9] and [30], respectively. We remark that in Gao and Wang's result it requires the technical condition P(X < −x) = o(P(X > x)), because of the certain dependence among {X i , i ≥ 1}; while in the independence structure, such a restriction can be easily dropped.…”

Section: 2mentioning

confidence: 99%

Asymptotics for ruin probabilities in Lévy-driven risk models with heavy-tailed claims

Yang¹,

Yuen²,

Liu³

2018

Journal of Industrial &Amp; Management Optimization

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Consider a bivariate Lévy-driven risk model in which the loss process of an insurance company and the investment return process are two independent Lévy processes. Under the assumptions that the loss process has a Lévy measure of consistent variation and the return process fulfills a certain condition, we investigate the asymptotic behavior of the finite-time ruin probability. Further, we derive two asymptotic formulas for the finite-time and infinite-time ruin probabilities in a single Lévy-driven risk model, in which the loss process is still a Lévy process, whereas the investment return process reduces to a deterministic linear function. In such a special model, we relax the loss process with jumps whose common distribution is long tailed and of dominated variation.

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Randomly weighted sums of subexponential random variables with application to capital allocation

Cited by 76 publications

References 30 publications

Asymptotics for a discrete-time risk model with Gamma-like insurance risks

Asymptotics for a discrete-time risk model with Gamma-like insurance risks

A Renewal Shot Noise Process with Subexponential Shot Marks

Asymptotics for ruin probabilities in Lévy-driven risk models with heavy-tailed claims

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