Forecasting Actuarial Processes with Generalized Linear Models

The method for statistical data analysis in insurance based on application of generalized linear models is studied. These models are extension of linear regression when distribution of random variable can differ from normal however belongs to the class of elliptical distributions. The model constructed can be linear or non-linear (for example, logit or probit). For parameters estimation of the models proposed the generalized least squares (GLS) or the Markov chain Monte Carlo methods are used. The main advantage of GLS is conversion of iterative algorithm which provides maximum likelihood parameter evaluations. The statistical values of losses in auto insurance are used to create the forecasting model for actuarial process selected. The model with Poisson distribution and exponential link function is acceptable for further use because it has minimum value of observational error and reliable value of risk approved by experts. Normal model with identity link function allows to find a result in one iteration with small value of observational error, but it showed “weak” predicted value of losses and impermissible risk assessment.

Publication year: 
2014
Issue: 
2
УДК: 
519.246.8
P14–20, Fig.1 Тabl. 6. Refs.7 titles
References: 

1. Тэпман Л.Н. Риски в экономике. — М.: ЮНИТИ, 2002. — 382 с.
2. Y.Y. Haimes and J.R. Santos, Risk modeling, assessment and management. New York: John Wiley & Sons, 2009, 447 p.
3. R. Kaas et al., Modern actuarial risk theory. New York: Kluwer Academic Publishers, 2002, 318 p.
4. J.F. Bouchaud and M. Potter, Theory of financial risk management. Cambridge: Cambridge University Press, 2001, 218 p.
5. P. McCullagh and J.A. Nelder, Generalized Linear Models. New York: Chapman & Hall, 1989, 526 р.
6. D. Collett, Modeling Binary Data. NewYork: Chapman & Hall, 2002, 388 p.
7. J. Gill, Generalized linear models — a unified approach. London: Sage Publications, 2001, 101 p.

References [transliteration]: 

1. Tėpman L.N. Riski v ėkonomike. – M.: I͡UNITI, 2002. – 382 s.
2. Y.Y. Haimes and J.R. Santos, Risk modeling, assessment and management. New York: John Wiley & Sons, 2009, 447 p.
3. R. Kaas et al., Modern actuarial risk theory. New York: Kluwer Academic Publishers, 2002, 318 p.
4. J.-F. Bouchaud and M. Potter, Theory of financial risk management. Cambridge: Cambridge University Press, 2001, 218 p.
5. P. McCullagh and J.A. Nelder, Generalized Linear Models. New York: Chapman & Hall, 1989, 526 р.
6. D. Collett, Modeling Binary Data. NewYork: Chapman & Hall, 2002, 388 p.
7. J. Gill, Generalized linear models – a unified approach. London: Sage Publications, 2001, 101 p.

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