On a compound Poisson risk model with dependence and in the presence of a constant dividend barrier

Cossette, Hélène; Marceau, Étienne; Marri, Fouad

doi:10.1002/asmb.1928

Cited by 12 publications

(7 citation statements)

References 26 publications

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“…Cossette, Marceau and Marri [17,18] consider the classical risk process with a constant dividend barrier and a dependence structure between claim sizes and interclaim times introduced through the Farlie-Gumbel-Morgenstern copula. They analyze the Gerber-Shiu function and the expected discounted dividend payments and then concentrate on exponentially distributed claim sizes investigating the impact of the dependence on ruin quantities.…”

Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Ragulina¹

2017

Modern Stoch. Theory Appl.

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The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by Farlie-Gumbel-Morgenstern copulas. In addition, dividends are paid to its shareholders according to a threshold dividend strategy. We derive integral and integro-differential equations for the Gerber-Shiu function and the expected discounted dividend payments until ruin. Next, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes. In particular, we find explicit formulas for the ruin probability in the model without either dividend payments or dependence as well as for the expected discounted dividend payments in the model without dependence. Finally, numerical illustrations are presented.

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Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Ragulina¹

2017

Modern Stoch. Theory Appl.

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“…To make up for this shortcoming (see [1,9,10,13], ), many works include in the risk model the dependence between certain dependence between certain random variables, in particular the variables claim amount and inter-claim time, thanks to the Farlie Gumbel Morgenstern copula (see, for example, references [5-8, 12, 18]). Although this copula is commonly used in the literature, encounters certain limitations.…”

Section: Introductionmentioning

confidence: 99%

“…, ≥ 0% the total number of claims recorded up to The aim of this work is to determine the integro-differential equation and the Laplace transform of the Gerber Shiu function in the risk model defined by the relation (1). The rest of the article is structured as follows: In section 2, we discuss the preliminaries of the risk model defined by the relation (1). In Section 3, we study the integro-differential equation satisfied by the Gerber Shiu function in the risk model defined by relation (1).…”

Section: Introductionmentioning

confidence: 99%

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

Kafando,

Ouedraogo,

Sawadogo

et al. 2024

AJTAS

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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.

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“…Risk models where shareholders receive dividends from their insurance company have been of great interest to researchers since De Finetti first considered dividend strategies in insurance dealing with a binomial model [12]. The classical risk model and its various modifications with different dividend strategies are investigated in a number of papers (see, e.g., [1,4,8,10,11,15,20,21,26,27,30] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Simple approximations for the ruin probability in the risk model with stochastic premiums and a constant dividend strategy

Ragulina¹

2020

Modern Stochastics: Theory and Applications

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We deal with a generalization of the risk model with stochastic premiums where dividends are paid according to a constant dividend strategy and consider heuristic approximations for the ruin probability. To be more precise, we construct five-and three-moment analogues to the De Vylder approximation. To this end, we obtain an explicit formula for the ruin probability in the case of exponentially distributed premium and claim sizes. Finally, we analyze the accuracy of the approximations for some typical distributions of premium and claim sizes using statistical estimates obtained by the Monte Carlo methods.

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On a compound Poisson risk model with dependence and in the presence of a constant dividend barrier

Cited by 12 publications

References 26 publications

The risk model with stochastic premiums, dependence and a threshold dividend strategy

The risk model with stochastic premiums, dependence and a threshold dividend strategy

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

Simple approximations for the ruin probability in the risk model with stochastic premiums and a constant dividend strategy

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