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Erscheinungsjahr: 
2021
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 9 [Issue:] 5 [Article No.:] 86 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-10
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
change of measure
exponential distribution
multidimensional risk process
non-life insurance
reinsurance
ruin probability
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