Acta Univ. Agric. Silvic. Mendelianae Brun. 2009, 57(6), 209-214 | DOI: 10.11118/actaun200957060209

Štatistická analýza zmesí v pravdepodobnosti ruinovania

Rastislav Potocký1, Milan Stehlík2
1 Ústav aplikovanej matematiky a statistiky, Univerzita Komenského, Mlynská Dolina, 842 48 Bratislava, Slovenská republika
2 Ústav aplikované statistiky, JKU Linz, Freistädter Straße 315, A-4040 Linz a. D., Rakousko

V našom príspevku sa zaoberáme aplikácou Cramer-Lundbergovej aproximácie pre škálové zmesy exponenciálnych rozdelení. Pri aplikácii uvedenej metódy na reálne dáta je potrebné otestovať vhodnosť modelu napr. testami Elr2 alebo Elrh uvedenými v príspevku. Prípad hornej a dolnej kontaminácie vedie na rozdielnu kvalitu aproximácie, preto je ich nutné starostlivo rozlišovať. Cramer-Lundbergova aproximácia je relatívne lepšia v prípade dolnej kontaminácie.

ELRH test, ELR2 test, pension pillar, ruin probability

Statistical analysis of mixtures underlying probability of ruin

If the hypothesis on exponentially distributed claims in a risk (or surplus) model is untenable then, in many cases, the assumption that they are mixtures of two (or more) exponentials is a suitable substitute. In the first part of the paper tests of homogeneity for exponentially distributed claims are discussed and their properties are stated. The statistical properties of parameter estimations for such claims are also mentioned. In the second part the classical Cramer-Lundberg ruin model is discussed when claims are distributed as mixtures of exponentials. Our attention is focussed primarily on assesment of accuracy of approximations obtained. Then our results are compared to those already known.

Grants and funding:

Research of Stehlík M. was partially supported by Project 50p14 "AKTION Czech Republic-Austria": Effective estimation supporting the risk assessment for Basel II".

Received: July 28, 2009; Published: October 7, 2014  Show citation

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Potocký, R., & Stehlík, M. (2009). Statistical analysis of mixtures underlying probability of ruin. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 57(6), 209-214. doi: 10.11118/actaun200957060209
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