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Optimality of barrier dividend strategy in a jump-diffusion risk model with debit interest

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Abstract

This paper investigates the optimal dividend problem in a jump-diffusion risk model with debit interest. In this model, the insurer could borrow money at a debit interest when the surplus turns negative. However, when the negative surplus attains a certain critical level, the business stops and absolute ruin happens at this moment. A sufficient condition under which the optimal dividend strategy is of barrier type is given in such a risk model. The main result relies on the smoothness of certain function arising from the dividend problem and we prove that it is twice continuously differentiable by the probability argument. Finally, numerical examples are given to illustrate the effects of the debit interest.

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Acknowledgements

This work was supported by MOE (Ministry of Education in China) Youth Project of Humanities and Social Sciences (Project Nos. 14YJCZH048,15YJCZH204), National Natural Science Foundation of China (Grant Nos. 11401436, 11601382).

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Authors and Affiliations

  1. College of Mathematical Science, Tianjin Normal University, Tianjin, 300387, People’s Republic of China

    Wei Wang

  2. School of Science, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Jingmin He

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  1. Wei Wang
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Correspondence to Jingmin He.

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Wang, W., He, J. Optimality of barrier dividend strategy in a jump-diffusion risk model with debit interest. Period Math Hung 82, 39–55 (2021). https://doi.org/10.1007/s10998-020-00338-x

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