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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

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

Klassifikation und Themen

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

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Burnecki, Krzysztof ; Teuerle, Marek A. ; Wilkowska, Aleksandra
• Ereignis: Veröffentlichung
• (wer): MDPI
• (wo): Basel
• (wann): 2021

Weitere Informationen

• DOI: doi:10.3390/risks9050086
• Handle: http://hdl.handle.net/10419/258174
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ