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De Finetti, B. (1957). Su un’Impostazione Alternativa Della Teoria Collettiva del Rischio, In International Congress of Actuaries, Proceedings of the Transactions of the XV International Congress of Actuaries (pp. 433-443). International Congress of Actuaries.

has been cited by the following article:

• TITLE: On the Expected Present Value of the Dividend Payments under a Dependence Structure Assumption

  AUTHORS: Ester C. Lari, Marina Ravera

  KEYWORDS: Risk Theory Models, Dependence Structure, Farlie-Gumbel-Morgenstern Copula, Dividends, Integral-Differential Equations

  JOURNAL NAME: Modern Economy, Vol.15 No.11, November 11, 2024

  ABSTRACT: We consider the classical risk theory model modified by a dependence structure between the amount of payments related to each claim and the time elapsed between two subsequent claims. In the classical Poisson model, the surplus definition is based on a Poisson compound process, which assumes independence between the arrival times of two subsequent claims and the amount of the related claims. In this paper, the classical model is modified to achieve more flexibility and adaptability to reality through a dependence structure. This dependence is defined by a generalized Farlie-Gumbel-Morgenstern copula (FGM). The classical risk theory model is further modified by the presence of a linear upper reflecting barrier; under different assumptions, we obtain the equations for the discounted dividend payments.