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.