Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model

Kiswendsida Mahamoudou Ouedraogo; Delwendé Abdoul-Kabir Kafando; Francois Xavier Ouedraogo; Pierre Clovis Nitiema

doi:doi:10.11648/j.ijsd.20241001.11

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Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model

Kiswendsida Mahamoudou Ouedraogo, Delwendé Abdoul-Kabir Kafando^*, Francois Xavier Ouedraogo, Pierre Clovis Nitiema

Published in International Journal of Statistical Distributions and Applications (Volume 10, Issue 1)

Received: 25 December 2023 Accepted: 4 January 2024 Published: 18 January 2024

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Abstract

This paper extends the compound Poisson risk model with a variable threshold dividend payment strategy and dependence between claims and inter-claim times, modeled via the Spearman copula. The objective is to establish the ultimate ruin probability in this framework. Following an introduction that motivates the study and highlights limitations of traditional risk models, the paper reviews relevant literature on risk models, dividend strategies, and copulas. Subsequently, it describes the extended model, including the dividend strategy and dependence structure. The Gerber-Shiu transform and Laplace transform of the ruin probability are then derived. Finally, the ultimate ruin probability is determined within the proposed model. Concluding remarks discuss the implications of the findings and suggest directions for future research. By considering a more realistic and comprehensive approach to financial risk modeling in insurance, this paper aims to contribute to the field of insurance risk management and provide industry professionals with improved tools for risk assessment and management.

Published in	International Journal of Statistical Distributions and Applications (Volume 10, Issue 1)
DOI	10.11648/j.ijsd.20241001.11
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Gerber-Shiu Function, Copula, Integro-Differential Equation, Ruin Probability

References

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APA Style

Ouedraogo, K. M., Kafando, D. A., Ouedraogo, F. X., Nitiema, P. C. (2024). Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model. International Journal of Statistical Distributions and Applications, 10(1), 1-9. https://doi.org/10.11648/j.ijsd.20241001.11

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ACS Style

Ouedraogo, K. M.; Kafando, D. A.; Ouedraogo, F. X.; Nitiema, P. C. Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model. Int. J. Stat. Distrib. Appl. 2024, 10(1), 1-9. doi: 10.11648/j.ijsd.20241001.11

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AMA Style

Ouedraogo KM, Kafando DA, Ouedraogo FX, Nitiema PC. Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model. Int J Stat Distrib Appl. 2024;10(1):1-9. doi: 10.11648/j.ijsd.20241001.11

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@article{10.11648/j.ijsd.20241001.11,
  author = {Kiswendsida Mahamoudou Ouedraogo and Delwendé Abdoul-Kabir Kafando and Francois Xavier Ouedraogo and Pierre Clovis Nitiema},
  title = {Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ijsd.20241001.11},
  url = {https://doi.org/10.11648/j.ijsd.20241001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241001.11},
  abstract = {This paper extends the compound Poisson risk model with a variable threshold dividend payment strategy and dependence between claims and inter-claim times, modeled via the Spearman copula. The objective is to establish the ultimate ruin probability in this framework. Following an introduction that motivates the study and highlights limitations of traditional risk models, the paper reviews relevant literature on risk models, dividend strategies, and copulas. Subsequently, it describes the extended model, including the dividend strategy and dependence structure. The Gerber-Shiu transform and Laplace transform of the ruin probability are then derived. Finally, the ultimate ruin probability is determined within the proposed model. Concluding remarks discuss the implications of the findings and suggest directions for future research. By considering a more realistic and comprehensive approach to financial risk modeling in insurance, this paper aims to contribute to the field of insurance risk management and provide industry professionals with improved tools for risk assessment and management.
},
 year = {2024}
}

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TY  - JOUR
T1  - Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model
AU  - Kiswendsida Mahamoudou Ouedraogo
AU  - Delwendé Abdoul-Kabir Kafando
AU  - Francois Xavier Ouedraogo
AU  - Pierre Clovis Nitiema
Y1  - 2024/01/18
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241001.11
DO  - 10.11648/j.ijsd.20241001.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241001.11
AB  - This paper extends the compound Poisson risk model with a variable threshold dividend payment strategy and dependence between claims and inter-claim times, modeled via the Spearman copula. The objective is to establish the ultimate ruin probability in this framework. Following an introduction that motivates the study and highlights limitations of traditional risk models, the paper reviews relevant literature on risk models, dividend strategies, and copulas. Subsequently, it describes the extended model, including the dividend strategy and dependence structure. The Gerber-Shiu transform and Laplace transform of the ruin probability are then derived. Finally, the ultimate ruin probability is determined within the proposed model. Concluding remarks discuss the implications of the findings and suggest directions for future research. By considering a more realistic and comprehensive approach to financial risk modeling in insurance, this paper aims to contribute to the field of insurance risk management and provide industry professionals with improved tools for risk assessment and management.

VL  - 10
IS  - 1
ER  -

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Author Information

Kiswendsida Mahamoudou Ouedraogo

Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

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Delwendé Abdoul-Kabir Kafando

Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso; Department of Mathematics, Université OUAGA 3S, Ouagadougou, Burkina Faso

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Francois Xavier Ouedraogo

Department of Mathematics, Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso

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Pierre Clovis Nitiema

Department of Mathematics, Université Thomas SANKARA, Ouagadougou, Burkina Faso

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Plain Text BibTeX RIS

APA Style

Ouedraogo, K. M., Kafando, D. A., Ouedraogo, F. X., Nitiema, P. C. (2024). Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model. International Journal of Statistical Distributions and Applications, 10(1), 1-9. https://doi.org/10.11648/j.ijsd.20241001.11

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ACS Style

Ouedraogo, K. M.; Kafando, D. A.; Ouedraogo, F. X.; Nitiema, P. C. Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model. Int. J. Stat. Distrib. Appl. 2024, 10(1), 1-9. doi: 10.11648/j.ijsd.20241001.11

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AMA Style

Ouedraogo KM, Kafando DA, Ouedraogo FX, Nitiema PC. Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model. Int J Stat Distrib Appl. 2024;10(1):1-9. doi: 10.11648/j.ijsd.20241001.11

Copy | Download

@article{10.11648/j.ijsd.20241001.11,
  author = {Kiswendsida Mahamoudou Ouedraogo and Delwendé Abdoul-Kabir Kafando and Francois Xavier Ouedraogo and Pierre Clovis Nitiema},
  title = {Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ijsd.20241001.11},
  url = {https://doi.org/10.11648/j.ijsd.20241001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241001.11},
  abstract = {This paper extends the compound Poisson risk model with a variable threshold dividend payment strategy and dependence between claims and inter-claim times, modeled via the Spearman copula. The objective is to establish the ultimate ruin probability in this framework. Following an introduction that motivates the study and highlights limitations of traditional risk models, the paper reviews relevant literature on risk models, dividend strategies, and copulas. Subsequently, it describes the extended model, including the dividend strategy and dependence structure. The Gerber-Shiu transform and Laplace transform of the ruin probability are then derived. Finally, the ultimate ruin probability is determined within the proposed model. Concluding remarks discuss the implications of the findings and suggest directions for future research. By considering a more realistic and comprehensive approach to financial risk modeling in insurance, this paper aims to contribute to the field of insurance risk management and provide industry professionals with improved tools for risk assessment and management.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Investigating the Impact of Variable Dividends and Tail Dependence in a Compound Poisson Risk Model
AU  - Kiswendsida Mahamoudou Ouedraogo
AU  - Delwendé Abdoul-Kabir Kafando
AU  - Francois Xavier Ouedraogo
AU  - Pierre Clovis Nitiema
Y1  - 2024/01/18
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241001.11
DO  - 10.11648/j.ijsd.20241001.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241001.11
AB  - This paper extends the compound Poisson risk model with a variable threshold dividend payment strategy and dependence between claims and inter-claim times, modeled via the Spearman copula. The objective is to establish the ultimate ruin probability in this framework. Following an introduction that motivates the study and highlights limitations of traditional risk models, the paper reviews relevant literature on risk models, dividend strategies, and copulas. Subsequently, it describes the extended model, including the dividend strategy and dependence structure. The Gerber-Shiu transform and Laplace transform of the ruin probability are then derived. Finally, the ultimate ruin probability is determined within the proposed model. Concluding remarks discuss the implications of the findings and suggest directions for future research. By considering a more realistic and comprehensive approach to financial risk modeling in insurance, this paper aims to contribute to the field of insurance risk management and provide industry professionals with improved tools for risk assessment and management.

VL  - 10
IS  - 1
ER  -

Copy | Download