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

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Résumé

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.

Mots-clés

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