Insurance market in Lithuania is evolving yet, but this process is quite rapid. The destination of this work – analysis of non life insurance in Lithuania, which we will dispense, when we will interpret statistical information of insurance, also we will analyze paying capacity of non life insurance companies. Insurance companies calculate future’s contribution using data of past period. It would be better to correct contribution according to predictive future’s number of contracts and loss. So the number of contracts and loss, signed by Lithuanian insurance companies each quarter, are studied as time series. Several time series models were created for three principal kinds of insurance (Motor Third Party Liability Insurance, Land vehicles other than railway rolling stock Insurance, Property Insurance) and the one that meets the reality best was selected. We will analyze variation of number of non life insurance companies, number of paid losses, number of signed contributions and number of contracts. After analyses of Insurance market’s indicators, we get strong tendency that Insurance market becomes more stable. After analysis of insurance companies’ paying capacity we got, that two close private companies - “Baltic Polis” and “Industrijos garantas” – was close to bankrupt in 2004 year. After forecasting number of Motor Third Party Liability Insurance’s and Land vehicles other than railway rolling stock Insurance’s contracts we got that Autoregressive model is the best for... [to full text]

Šiame darbe pateikiami standartiniai modeliai bei priemonės, kurios plačiai taikomos ne gyvybės draudime. Vėliau, šių modelių bei priemonių pagalba atliekama žalų atėjimo momentų ir žalų dydžių statistinė analizė realiems ne gyvybės draudimo duomenims. Rezultatas – žalų skaičiaus procesą aprašantis Puasono proceso modelis su intensyvumo parametro pasikeitimu bei žalų dydžius apibūdinanti pasiskirstymo funkcija. Intensyvumo parametro pasikeitimo taškas rastas [2] darbe pateiktu algoritmu. / The subject of the research is statistical analysis of claim arrival times and claim sizes in non-life insurance. First, I present some standard models and tools of non-life insurance mathematics. Also, I introduce the statistical tools for analysing the claim number and size processes, such as QQ plots, Mean excess plots, etc. Second, the statistical analysis of claim arrival times and claim sizes for the 4 years real car insurance data are done. Results show that homogeneous Poisson process is a suitable model for the arrivals for shorter periods of time (such as one year). In addition, claim sizes data reveals heavy-tailedness and skewedness to the right. Finally, the change point problem in the rate parameter of the Poisson process was studied. The change point was detected using algorithm given in [2].