2020
DOI: 10.3390/math8040511
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On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Abstract: In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount … Show more

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Cited by 29 publications
(29 citation statements)
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“…Some scholars also measure the sustainability of the UEBEI funds through actuarial balance; for example, Mircea et al [20] developed some models for mortality rates and pricing considering the longevity risk; they also expanded some models for the securitization of longevity bonds or loans to increase the sustainability of pension funds from the perspective of longevity risk (Mircea et al [20]; Lin and Tsai [21]; Yu et al [22]). Metzger [23] analyzed the medium-term sustainability of the Swiss old-age pension scheme by estimating a "Swedish" actuarial balance sheet, which compares pension liabilities with the explicit and implicit assets of the pension scheme.…”
Section: Mathematical Problems In Engineeringmentioning
confidence: 99%
“…Some scholars also measure the sustainability of the UEBEI funds through actuarial balance; for example, Mircea et al [20] developed some models for mortality rates and pricing considering the longevity risk; they also expanded some models for the securitization of longevity bonds or loans to increase the sustainability of pension funds from the perspective of longevity risk (Mircea et al [20]; Lin and Tsai [21]; Yu et al [22]). Metzger [23] analyzed the medium-term sustainability of the Swiss old-age pension scheme by estimating a "Swedish" actuarial balance sheet, which compares pension liabilities with the explicit and implicit assets of the pension scheme.…”
Section: Mathematical Problems In Engineeringmentioning
confidence: 99%
“…Proof of Corollary 3. Firstly, if V satisfies conditions (c), (d), and (e), for any k ≥ 1, then both (31) and (32) hold. Now let us show this proof process as follows.…”
Section: Corollarymentioning
confidence: 99%
“…Following the proof of Corollary 3 by using formula (40), we only need to prove irdly, if V satisfies conditions (c), (d), and (g), for any k ≥ 1, we can also have formulas (31) and (32). e proof process is as follows.…”
Section: Corollarymentioning
confidence: 99%
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“…Pérez and Yamazaki [25] and Noba et al [26] study the optimality of periodic barrier strategies for a spectrally positive Lévy process and Lévy risk processes, respectively. Other relevant literature can be found in Yang and Deng [27], Dong and Zhou [28], Dong and Zhao [29], Yang et al [30], Liu et al [31], and Yu et al [32].…”
Section: Introductionmentioning
confidence: 99%