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Research Article |

On Sparre Andersen Model with Partial Premium Payment Strategy to Shareholders with Dependence via Sperman Copula

This paper is based on the Poisson composite risk model, popularised for its flexibility in modelling loss occurrences. However, it innovates by incorporating a strategy of distributing dividends to shareholders, adding a realistic dimension to the financial implications. A key element is the introduction of a constant threshold 'b', representing a critical amount beyond which claims become significant. This threshold makes it possible to distinguish between small, routine claims and major events with a significant impact on reserves. In addition, the model introduces a dependency between the amount of claims and the time between claims via the Spearman copula. This copula captures the non-independence often observed in insurance data, where large claims tend to be followed by claim-free periods or vice versa. The analysis then focuses on the integro-differential equation associated with the model, which describes the evolution of Gerber's Shiu function, a fundamental element in assessing the reserve required to cover future obligations. The Laplace transform of this function is also studied, providing valuable information on the distribution of the long-term reserve.

Gerber-Shiu Functions, Dependence, Spearman Copula, Dividends, Integro-Differential Equation

APA Style

Kafando, D. A., Ouedraogo, F. X., Sawadogo, L., Ouedraogo, K. M., Nitiema, P. C. (2024). On Sparre Andersen Model with Partial Premium Payment Strategy to Shareholders with Dependence via Sperman Copula. American Journal of Theoretical and Applied Statistics, 13(1), 1-7. https://doi.org/10.11648/j.ajtas.20241301.11

ACS Style

Kafando, D. A.; Ouedraogo, F. X.; Sawadogo, L.; Ouedraogo, K. M.; Nitiema, P. C. On Sparre Andersen Model with Partial Premium Payment Strategy to Shareholders with Dependence via Sperman Copula. Am. J. Theor. Appl. Stat. 2024, 13(1), 1-7. doi: 10.11648/j.ajtas.20241301.11

AMA Style

Kafando DA, Ouedraogo FX, Sawadogo L, Ouedraogo KM, Nitiema PC. On Sparre Andersen Model with Partial Premium Payment Strategy to Shareholders with Dependence via Sperman Copula. Am J Theor Appl Stat. 2024;13(1):1-7. doi: 10.11648/j.ajtas.20241301.11

Copyright © 2024 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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