Ruin probability for the insurer-reinsurer model for exponential claims: A probabilistic approach

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Risks ; ISSN: 2227-9091 ; Volume: 9 ; Year: 2021 ; Issue: 5 ; Pages: 1-10 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft
• Subject: change of measure ; exponential distribution ; multidimensional risk process ; non-life insurance ; reinsurance ; ruin probability

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Burnecki, Krzysztof ; Teuerle, Marek A. ; Wilkowska, Aleksandra
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2021

Further information

• DOI: doi:10.3390/risks9050086
• Handle: http://hdl.handle.net/10419/258174
• Last update: 10.03.2025, 11:42 AM CET