On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Yu, Wenguang; Guo, Peng; Wang, Qi; Guan, Guofeng; Yang, Qing; Huang, Yubing; Yu, Xinliang; Jin, Boyi; Cui, Chaoran

doi:10.3390/math8040511

Cited by 29 publications

(28 citation statements)

References 49 publications

(59 reference 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%

The New Fertility Policy and the Actuarial Balance of China Urban Employee Basic Endowment Insurance Fund Based on Stochastic Mortality Model

Xie

Zhang

et al. 2020

Mathematical Problems in Engineering

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This study aims to investigate the impact of China’s new fertility policy on the actuarial balance of its Urban Employee Basic Endowment Insurance (UEBEI) fund, with stochastic mortality model included to address the longevity risk. Combined with the latest UEBEI policy, this paper constructs an actuarial balance model and introduces the growth rate of wage, the age of employment and the age of retirement, the rate of payment, the rate of replacement, the annual rate of pension adjustment, and the population in terms of age into the model, which arise from the rate of payment, average wage, and personal and social factors. This study uses the sixth population census data by age group and gender to employ empirical analysis. The sensitivity analysis of China’s basic pension insurance fund balance is made. It is concluded that the increase in the growth rate of wage caused by social factors, the increase of fund investment returns, the delay of retirement, and the increase in the fund collection rate are all conducive to the sustainability of the UEBEI fund.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

The New Fertility Policy and the Actuarial Balance of China Urban Employee Basic Endowment Insurance Fund Based on Stochastic Mortality Model

Xie

Zhang

et al. 2020

Mathematical Problems in Engineering

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“…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%

“…Recently, a qualitative study by Yang et al [31] described a discrete-time insurance risk model with insurance and financial risks. en, a key study is that of Yu et al [32], which proposed a new risk model called compound Poisson risk model by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. Furthermore, the risk model can be further extended and applied to a wider range of practical problems.…”

Section: Introductionmentioning

confidence: 99%

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The Limit Theorems for Function of Markov Chains in the Environment of Single Infinite Markovian Systems

Huang

Meng

et al. 2020

Mathematical Problems in Engineering

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This paper is intended to study the limit theorem of Markov chain function in the environment of single infinite Markovian systems. Moreover, the problem of the strong law of large numbers in the infinite environment is presented by means of constructing martingale differential sequence for the measurement under some different sufficient conditions. If the sequence of even functions gnx,n≥0 satisfies different conditions when the value ranges of x are different, we have obtained SLLN for function of Markov chain in the environment of single infinite Markovian systems. In addition, the paper studies the strong convergence of the weighted sums of function for finite state Markov Chains in single infinitely Markovian environments. Although the similar conclusions have been carried out, the difference results performed by previous scholars are that we give weaker different sufficient conditions of the strong convergence of weighted sums compared with the previous conclusions.

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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%

Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend

Guo

Wang

et al. 2021

Adv Differ Equ

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In this paper, we model the insurance company’s surplus by a compound Poisson risk model, where the surplus process can only be observed at random observation times. It is assumed that the insurer observes its surplus level periodically to decide on dividend payments and capital injection at the interobservation time having an $\operatorname{Erlang}(n)$ Erlang ( n ) distribution. If the observed surplus level is greater than zero but less than injection line $b_{1} > 0$ b 1 > 0 , the shareholders should immediately inject a certain amount of capital to bring the surplus level back to the injection line $b_{1}$ b 1 . If the observed surplus level is larger than dividend line $b_{2}$ b 2 ($b_{2} > b_{1}$ b 2 > b 1 ), any excess of the surplus over $b_{2}$ b 2 is immediately paid out as dividends to the shareholders of the company. Ruin is declared when the observed surplus level is negative. We derive the explicit expressions of the Gerber–Shiu function, the expected discounted capital injection, and the expected discounted dividend payments. Numerical illustrations are also given to analyze the effect of random observation times on actuarial quantities.

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On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Cited by 29 publications

References 49 publications

The New Fertility Policy and the Actuarial Balance of China Urban Employee Basic Endowment Insurance Fund Based on Stochastic Mortality Model

The New Fertility Policy and the Actuarial Balance of China Urban Employee Basic Endowment Insurance Fund Based on Stochastic Mortality Model

The Limit Theorems for Function of Markov Chains in the Environment of Single Infinite Markovian Systems

Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend

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