Dividend Strategy For Risk Model With Generalized F-G-M Copula Function

For the classical compound Poisson risk model, it is always assumed that the claim amounts and the inter-claim times are independent. However, in fact, some dependencies may exist in the claim amounts and the inter-claim times. This risk model is one kind of the dependent risk models. The dependent risk model has been extensively studied. In recent years, scholars proposed a dependence structure for the claim amounts and the inter-claim times based on a copula. Later, scholars studied an extension of the compound Poisson risk model with the dependence structure defined by a generalized Farlie-Gumbel-Morgenstern copula and derived its Gerber-Shiu functions. Furthermore, for the risk model with the dependence structure defined by a generalized Farlie-Gumbel-Morgenstern copula, scholars considered its Gerber-Shiu functions under constant barrier strategy.In this paper, we continue to study the compound Poisson risk model with the de-pendence structure defined by a generalized Farlie-Gumbel-Morgenstern copula under three dividend strategies:the barrier strategy, the threshold strategy and the hybrid s-trategy. The integro-differential equations with certain boundary conditions satisfied by the expected discounted value of dividend payments under three dividend strategies are derived respectively. Besides, we also derive integro-differential equations with bound-ary conditions for the Gerber-Shiu functions under a hybrid dividend strategy. Above all, when the claim amounts are exponentially distributed, we show minutely that the integro-differential equations of the expected discounted value of dividend payments can be converted to differential equations. However, it remains to be solved for other cases.This article is organized as follows.In Chapter1, we introduce the background knowledge of the problem involved in this paper.In Chapter2, we introduce the compound Poisson risk model with a generalized Farlie-Gumbel-Morgenstern copula.In Chapter3. we first derive the integro-differential equations for the expected dis-counted value of dividend payments under three dividend strategies, respectively. Then, we convert the integro-differential equations of the expected discounted value of dividend payments to differential equations, when the claim amounts are exponentially distribut-ed. We also give several examples to show how to calculate the specific expression of the expected discounted value of dividend payments. In Chapter4, we give the integro-differential equations and the boundary conditions for the Gerber-Shiu functions under a hybrid dividend strategy.