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Transactions: INTERNATIONAL JOURNAL of MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES
Transactions ID Number: 19-523
Full Name: Meelis Käärik
Position: Doctor (Researcher)
Age: ON
Sex: Male
Address: J. Liivi 2 - 513, Tartu
Country: ESTONIA
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E-mail address: meelis.kaarik@ut.ee
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Title of the Paper: On claim size fitting and rough estimation of risk premiums based on Estonian traffic insurance example
Authors as they appear in the Paper: Meelis Käärik, Merili Umbleja
Email addresses of all the authors: meelis.kaarik@ut.ee, a31965@ut.ee
Number of paper pages: 8
Abstract: Financial and actuarial mathematics offer various problems related to estimation of distributions.,Classical models for premium calculations usually require some estimates for both the distribution of individual claim size and also the number of claims. In this work we mainly consider the problem of estimation of individual claim size, but also some basics on the fitting of the distribution of claim number and tools to find rough estimates for risk premium are provided to complete the model. Most of the ideas are applied to a real-life data from Estonian traffic insurance from mid 2006 to mid 2007. The research was initiated by Estonian Traffic Insurance Fund and therefore is of practical importance. The first four sections of the article focus on the distribution of the individual claim size, we search answers for questions like: * what candidate distributions to use for fitting the data? * what fitting techniques to use? * how to measure which of the proposed ca!
ndidates is best? We choose five commonly used distributions as possible estimates: lognormal, Pareto, Weibull, beta and gamma. The fitting techniques are based on moment matching or maximum likelihood estimators. For testing goodness of fit (GOF) several classical tests including Chi-square test and Kolmogorov-Smirnov test are used. The accuracy of our approach is evaluated by matching the first and second moments and by plotting PDF-s and CDF-s. % The last section of the article focuses on estimation of the the claim amount for the whole portfolio and also describes a simple idea how the standard deviance principle can be used to find a first rough estimate for risk premium when the available history is limited. The estimates for risk premiums are found by the classical collective risk model. Several simplifications are made due to the lack of information, turns out that the resulting estimates are comparable with those used in practice by insurance companies.
Keywords: Estimation of distributions, Heavy-tailed distributions, Goodness-of-fit tests, Collective risk model, Premium calculation
EXTENSION of the file: .pdf
Special (Invited) Session: Estimation of claim size distributions in Estonian traffic insurance
Organizer of the Session: 654-469
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