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Ruin Probability for the Insurer–Reinsurer Model for Exponential Claims: A Probabilistic Approach

Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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Academic Editor: Anatoliy Swishchuk
Received: 19 February 2021 / Revised: 21 April 2021 / Accepted: 25 April 2021 / Published: 3 May 2021
In this paper, we consider a two-dimensional risk process in which the companies split each claim and premium in a fixed proportion. It serves as a classical framework of a quota-share reinsurance contract for a given business line. Such a contract reduces the insurer’s exposure to the liabilities created through its underwriting activities. For the analyzed model, we derive a joint infinite-time ruin probability formula for exponentially distributed claims. To this end, we apply a change of measure technique. We illustrate the admissible range of parameters of the risk process. We also justify our result using Monte Carlo simulations and compare it with Theorem 2 in Avram, Palmowski and Pistorius [Insurance: Mathematics and Economics 42 (2008) 227], which was obtained by explicitly inverting a Laplace transform of the ruin probability. Our formula leads to a correction of that result. Finally, we note that the obtained formula leads to efficient approximation of the ruin probability for other claim amount distributions using De Vylder’s idea. View Full-Text
Keywords: non-life insurance; multidimensional risk process; ruin probability; change of measure; exponential distribution; reinsurance non-life insurance; multidimensional risk process; ruin probability; change of measure; exponential distribution; reinsurance
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MDPI and ACS Style

Burnecki, K.; Teuerle, M.A.; Wilkowska, A. Ruin Probability for the Insurer–Reinsurer Model for Exponential Claims: A Probabilistic Approach. Risks 2021, 9, 86. https://0-doi-org.brum.beds.ac.uk/10.3390/risks9050086

AMA Style

Burnecki K, Teuerle MA, Wilkowska A. Ruin Probability for the Insurer–Reinsurer Model for Exponential Claims: A Probabilistic Approach. Risks. 2021; 9(5):86. https://0-doi-org.brum.beds.ac.uk/10.3390/risks9050086

Chicago/Turabian Style

Burnecki, Krzysztof, Marek A. Teuerle, and Aleksandra Wilkowska. 2021. "Ruin Probability for the Insurer–Reinsurer Model for Exponential Claims: A Probabilistic Approach" Risks 9, no. 5: 86. https://0-doi-org.brum.beds.ac.uk/10.3390/risks9050086

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