Estimation of Generalized Linear Models Using Bayesian Approach in Actuarial Modeling

The article deals with Bayesian methodology for estimating unknown parameters of mathematical models and the method of analysis statistic data in insurance based on generalized linear models. These models are extension of linear regression when distribution of random variable can differ from normal. For estimating the parameters of proposed models classical and Bayesian approach were used. The main advantage of Bayesian approach is its ability to generate not only accurate estimates but probability distributions too. It gives the opportunity to describe in details the structure and the nature of investigated models. The value of damages in autoinsurance were hired for creating the forecasting model of actuarial process. The model with Poisson distribution and an exponential link function turned out to be acceptable for further use because it has minimum value of observation error and reliable estimate for risk value which was received using Bayesian approach. A normal model with identity link function allows to generate a result after one iteration with small value of observation error but “weak” predicted value of losses and poor risk assessment.

Publication year: 
2014
Issue: 
6
УДК: 
519.246.8
С. 49–55.Іл. 2. Табл. 3. Бібліогр.: 10 назв.
References: 

1. Бідюк П.І., Романенко В.Д., Тимощук О.Л. Аналіз часових рядів. — К.: Політехніка, 2013. — 600 с.
2. R.H. Shumway and D.S. Stoffer, Time series analysis and its applications. New York: Springer, 2006, 598 p.
3. A. Romano and G. Secundo, Dynamic learning methods. New York: Springer, 2009, 190 p.
4. P. McCullagh and J.A. Nelder, Generalized Linear Models. New York: Chapman & Hall, 1989, 526 р.
5. R.S. Tsay, Analysis of financial time series. New Jersey: John Wiley & Sons, Inc., 2010, 715 p.
6. J. Besag, “Markov Chain Monte Carlo for Statistical Inference”, Center for Statistics and the Social Sciences, Working Paper no. 9, 25 p., 2001.
7. D.J.C. MacKay, Information Theory, Inference, and Learning Algorithms. Cambridge: Cambridge University Press, 2003, 640 p.
8. N. da Costa Lewis. Market Risk Modeling. Applied Statistical Methods for Practitioners. London: Risk Waters Group Ltd., 2003, 238 p.
9. N. Bergman, “Recursive Bayesian Estimation: Navigation and Tracking Applications”, Linkoping University (Sweden), TR no. 579, 219 p., 1999.
10. Трухан С.В., Бідюк П.І. Прогнозування актуарних процесів за допомогою узагальнених лінійних моделей // Наукові вісті НТУУ “КПІ”. — 2014. — № 2. — С. 14—20.

References [transliteration]: 

1. Bidi͡uk P.I., Romanenko V.D., Tymoshchuk O.L. Analiz chasovykh ri͡adiv. – K.: Politekhnika, 2013. – 600 s.
2. R.H. Shumway and D.S. Stoffer, Time series analysis and its applications. New York: Springer, 2006, 598 p.
3. A. Romano and G. Secundo, Dynamic learning methods. New York: Springer, 2009, 190 p.
4. P. McCullagh and J.A. Nelder, Generalized Linear Models. New York: Chapman & Hall, 1989, 526 р.
5. R.S. Tsay, Analysis of financial time series. New Jersey: John Wiley & Sons, Inc., 2010, 715 p.
6. J. Besag, “Markov Chain Monte Carlo for Statistical Inference”, Center for Statistics and the Social Sciences, Working Paper no. 9, 25 p., 2001.
7. D.J.C. MacKay, Information Theory, Inference, and Learning Algorithms. Cambridge: Cambridge University Press, 2003, 640 p.
8. N. da Costa Lewis. Market Risk Modeling. Applied Statistical Methods for Practitioners. London: Risk Waters Group Ltd., 2003, 238 p.
9. N. Bergman, “Recursive Bayesian Estimation: Navigation and Tracking Applications”, Linkoping University (Sweden), TR no. 579, 219 p., 1999.
10. Trukhan S.V., Bidi͡uk P.I. Prohnozuvanni͡a aktuarnykh prot͡sesiv za dopomohoi͡u uzahal′nenykh liniĭnykh modeleĭ // Naukovi visti NTUU “KPI”. – 2014. – # 2. – S. 14–20.

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