Research Article
Improving Risk Assessment and Pricing with Dividend Barriers and Dependence Modelling: An Extension of the Cramer-Lundberg Model with Spearman Copulas
Kiswendsida Mahamoudou Ouedraogo,
Delwendé Abdoul-Kabir Kafando*,
Frédéric Bere,
Pierre Clovis Nitiema
Issue:
Volume 9, Issue 1, April 2024
Pages:
1-8
Received:
7 December 2023
Accepted:
28 December 2023
Published:
11 January 2024
Abstract: The compound Poisson risk model is a probabilistic model commonly used to evaluate the financial risk of an insurance company. This model assumes that claims arrive according to a Poisson process and that claim sizes follow an independent probability distribution. This paper presents an extension of this model, incorporating a dividend payment strategy with a constant threshold b. This extension allows for a better representation of the reality of insurance companies, which typically pay dividends to their shareholders. The traditional assumption of independence between claim sizes and interclaim intervals is also relaxed in this extension. This relaxation allows for recognition of the potential dependence between these variables, which can have a significant impact on the company’s ruin probability. The Spearman copula is used to model the dependent structure between claim sizes and interclaim intervals. The Spearman copula is a function that measures the degree of dependence between two variables. It is used in many fields, including insurance, finance, and statistics. The study focuses on the Laplace transform of the adjusted penalty function. The adjusted penalty function is a function that allows for the determination of the company’s ruin probability. The results of the study show that the dependence between claim sizes and interclaim intervals can have a significant impact on the company’s ruin probability. In particular, positive dependence between these variables can increase the ruin probability.
Abstract: The compound Poisson risk model is a probabilistic model commonly used to evaluate the financial risk of an insurance company. This model assumes that claims arrive according to a Poisson process and that claim sizes follow an independent probability distribution. This paper presents an extension of this model, incorporating a dividend payment stra...
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Research Article
Mathematical Modeling of COVID-19 with Chronic Patients and Sensitivity Analysis
Windjiré Somé*,
Germain Kaboré,
Kassiénou Lamien,
Ismaël Diallo,
Ousséni So,
Blaise Somé
Issue:
Volume 9, Issue 1, March 2024
Pages:
9-19
Received:
12 March 2024
Accepted:
7 April 2024
Published:
9 May 2024
Abstract: Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are taking part in the fight through mathematical modeling in various approaches. Ordinary derivative compartmental modeling approache is one of the techniques widely used in epidemiological modeling. This paper presents a mathematical contribution to fight against COVID-19 using a compartmental SQEICRS model. This model takes into account five stages. In particular, the role of chronic diseases on the dynamique of COVID-19, is focused. A mathematical analysis of the model has been carried out, and shows that the model is well-posed in the biological and mathematical sense. Aspects such as existence, equilibrium points and their stability, the basic reproduction number R0and sensitivity anlysis have been discussed. Sensitivity analysis allowed us to identify the parameters which contribute to the spread of the disease, including the chronicity rate due to chronic diseases. The direction of disease propagation was also determined according to R0. Finally, the numerical results with Matlab are in conformity with theoretical results.
Abstract: Human health is constantly threatened by the appearance and resurgence of several diseases, as shown by recent epidemics. COVID-19 was one of the epidemics that left its mark on the world in terms of economic and human damages. In the search for solution to this pandemic, the scientific community is involved in all its diversity. Mathematicians are...
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