Zastosowanie rozkładu α-stabilnego do modelowania zmian cen ubezpieczeń
Application of the α-stable distribution to modeling changes in insurance prices

Summary/Abstract: The main purpose of this work is attempt of application α-stable distribution with its parameters es- timation to the empirical distribution of changes in insurance price indexes in Poland. The α-stable distribution, although commonly used in finance, is not very common in insurance. It is use mainly in insurance risk analysis and extreme value theory (due to its properties: “heavy tails”, leptocurtility) rather than directly in insurance prices. Literature analysis shows that insurance prices have not yet been the subject of a review into the verifiability of the possibility of applying the α-stable distribution (opposed to the prices of financial assets in different markets) and insurance prices are an importantdeterminant of the demand for insurance. As part of this work, parameters for the stable distribution of changes in insurance price indicators in Poland were estimated. The estimated distribution param- eters allowed distribution to be stable matched with empirical data, which was confirmed by Anderson– Darling test. The study confirmed that the stable distribution class can be very useful for describing empirical data of financial time series such as insurance price changes in Poland.

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