A discrete-time dual risk model with dependence based on a Poisson INAR(1) process

Lihong Guan; Xiaohong Wang; Lihong Guan; Xiaohong Wang

doi:10.3934/math.20221141

AIMS Mathematics

2022, Volume 7, Issue 12: 20823-20837. doi: 10.3934/math.20221141

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A discrete-time dual risk model with dependence based on a Poisson INAR(1) process

Lihong Guan ^{1
,
,},
Xiaohong Wang ²

1.
School of Science, Changchun University, Changchun 130022, China
2.
Mathematics and Computer College, Jilin Normal University, Siping 136000, China

Received: 28 July 2022 Revised: 11 September 2022 Accepted: 19 September 2022 Published: 08 October 2022
MSC : 62P05, 91B30, 97M30

In this paper, we consider an extension of the classical discrete-time dual risk model, in which the first-order integer-valued autoregressive (INAR(1)) process with Poisson distributed innovations is utilized to fit the temporal dependence between the number of gains for each period. We derive the explicit expression for a function that allows us to find the Lundberg adjustment coefficient and obtain the Lundberg approximation formula for ruin probability. Some numerical examples are provided to illustrate our main results.
- dual risk model,
- INAR(1) process,
- Lundberg adjustment coefficient,
- ruin probability
Citation: Lihong Guan, Xiaohong Wang. A discrete-time dual risk model with dependence based on a Poisson INAR(1) process[J]. AIMS Mathematics, 2022, 7(12): 20823-20837. doi: 10.3934/math.20221141

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Abstract

In this paper, we consider an extension of the classical discrete-time dual risk model, in which the first-order integer-valued autoregressive (INAR(1)) process with Poisson distributed innovations is utilized to fit the temporal dependence between the number of gains for each period. We derive the explicit expression for a function that allows us to find the Lundberg adjustment coefficient and obtain the Lundberg approximation formula for ruin probability. Some numerical examples are provided to illustrate our main results.

References

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