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

Krzysztof Burnecki, Marek Teuerle and Aleksandra Wilkowska
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Aleksandra Wilkowska: Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Risks, 2021, vol. 9, issue 5, 1-10

Abstract: 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.

Keywords: non-life insurance; multidimensional risk process; ruin probability; change of measure; exponential distribution; reinsurance (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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