Geodesic
De Vylder type approximation of the ruin probability for the insurer-reinsurer model
Mathematica Applicanda, Tome 47 (2019) no. 1, pp. 5-24.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this article we introduce a De Vylder type of approximation of the ruin probability for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. Such a process is usually associated with the insurer-reinsurer model. Applying De Vylder's idea to the risk process we obtain an approximation of the ruin probability for an arbitrary claim amount distribution only assuming that the third moment exists. We check the performance of the approximation by means of the Monte Carlo simulations studying several typical claim amount distributions. All results show that the proposed approximation yields very small relative errors. Finally, we illustrate the approximation by considering real-world loss data obtained from a Polish insurance company.
DOI : 10.14708/ma.v47i1.6417
Classification : 91B30, 62P05.
Mots-clés : ruin probability, two-dimensional risk process, De Vylder approximation. 
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Krzysztof Burnecki; Marek A. Teuerle; Aleksandra Wilkowska. De Vylder type approximation of the ruin probability for the insurer-reinsurer model. Mathematica Applicanda, Tome 47 (2019) no. 1, pp.  5-24. doi : 10.14708/ma.v47i1.6417. http://geodesic.mathdoc.fr/articles/10.14708/ma.v47i1.6417/

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