Methods of building mathematical models ofactuarial processes
DOI:
https://doi.org/10.15587/1729-4061.2015.36486Keywords:
generalized linear models, connection function, remains, Monte Carlo methods, the Bayesian approachAbstract
We have suggested a set of methods for designing mathematical models ofactuarial processes and an algorithm for evaluating unknown parameters with application of the Bayesian approach. The generalized linear models that represent expansion of the linear regression in cases when distribution of random variables differs from the norm are used as mathematical tools. This facilitates a detailed description of the structure and content of the researched model.
Real statistical data on the losses in the car insurance industry and the suggested methods have laid the basis for building a prognostic model of the actuarial process. A model using the Poisson distribution law and exponential function of communication has proved to be suitable for future use. It is confirmed by a minimal error magnitude and reliable estimates of parameters of generalized linear models obtained with the use of the Bayesian approach. We have determined that the normal model with anidentical connection function allows obtaining a result within one iteration with a slight relative errorbut with inaccurate predicted values of losses. Further studies require solution of the following tasks: analyzing and usinga set of risk factors that impact insurance cases, applying methods of intellectual data analysis in modeling, and forecasting actuarial processes.
References
- Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. Nesbitt, C. J. (1986). Actuarial mathematics. Itasca (Illinois): Society of Actuaries, 624.
- Oleksyuk, О. S. Financial decision support system on the macro level. (1998). Kyiv: Naukova dymka, 508.
- Bidyuk, P., Gozhiy, O., Korshevnyuk, L. (2011). Design of computer based decision support systems. Petro Mohyla Black Sea State University, 320.
- Gill, J. (2001) Generalized linear models: a unified approach. USA: New Delli, 110 p.
- Bidyuk, P., Borusevich, A. (2008). Estimation parameters of models using Monte Carlo Markov Chain technique. Petro Mohyla Black Sea State University, 77, 2–37.
- Tsay, S. (2010). Financial time series analysis. Hoboken (New Jersey): John Wiley & Sons, 715.
- Enders, W. (1994). Applied econometric time series. New York: Wiley and Sons, 433.
- Bidyuk, P., Romanenko, V., Tumoshchyk, O. (2013). Time series analysis. NTUU ‘KPI’, 115–158.
- McCullagh, P., Nelder, J. A. (1990). Generalized Linear Models. New York: Chapman & Hall, 526. doi: 10.1007/978-1-4899-3242-6
- Trukhan, S., Bidyuk, P. (2014). Forecasting of actuarial processes using Generalized linear models. Naukovi Visti NTUU ‘KPI’, 2, 14–20.
- Bergman, N. (1999). Recursive Bayesian Estimation: Navigation and Tracking Applications. Linkoping University (Sweden), 579, 219.
- Besag, J. (2001). Markov Chain Monte Carlo for Statistical Inference. Working Paper, Center for Statistics and the Social Sciences, 9, 25.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Світлана Віталіївна Трухан, Петро Іванович Бідюк
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
