On a dependent risk model perturbed by mixed-exponential jump-diffusion processes

Zhipeng Liu; Cailing Li; Zhenhua Bao; Zhipeng Liu; Cailing Li; Zhenhua Bao

doi:10.3934/math.2025452

AIMS Mathematics

2025, Volume 10, Issue 4: 9882-9899. doi: 10.3934/math.2025452

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Research article

On a dependent risk model perturbed by mixed-exponential jump-diffusion processes

1.
School of Economics, Liaoning University of International Business and Economics, Dalian 116052, China
2.
School of Mathematics, Liaoning Normal University, Dalian 116081, China

Received: 02 December 2024 Revised: 22 March 2025 Accepted: 15 April 2025 Published: 27 April 2025
MSC : 91B30, 91B70

In the present paper, we investigate a dependent risk model perturbed by a mixed-exponential jump-diffusion process, in which the claim inter-arrival times and claim sizes are dependent through Farlie-Gumbel-Morgenstern (FGM) copula. The expected discounted penalty (EDP) functions are studied when ruin is caused by a claim or the jump-diffusion process. The Laplace transforms satisfied by the EDP functions are obtained, then we give the corresponding defective renewal equations. The analytical expressions for the EDP functions are derived when the claim sizes follow exponential distributions, and a numerical example for the ruin probabilities are also provided.
- expected discounted penalty function,
- dependence,
- mixed-exponential jump-diffusion process,
- defective renewal equation,
- Laplace transform
Citation: Zhipeng Liu, Cailing Li, Zhenhua Bao. On a dependent risk model perturbed by mixed-exponential jump-diffusion processes[J]. AIMS Mathematics, 2025, 10(4): 9882-9899. doi: 10.3934/math.2025452

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Abstract

In the present paper, we investigate a dependent risk model perturbed by a mixed-exponential jump-diffusion process, in which the claim inter-arrival times and claim sizes are dependent through Farlie-Gumbel-Morgenstern (FGM) copula. The expected discounted penalty (EDP) functions are studied when ruin is caused by a claim or the jump-diffusion process. The Laplace transforms satisfied by the EDP functions are obtained, then we give the corresponding defective renewal equations. The analytical expressions for the EDP functions are derived when the claim sizes follow exponential distributions, and a numerical example for the ruin probabilities are also provided.

References

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