Geometric-Gamma Collective Modified Value-at-Risk Model in Life Insurance Risk

  • Authors

    • Muhammad Iqbal Al-Banna Ismail
    • Sukono .
    • Abdul Talib BIN Bon
    • Yuyun Hidayat
    • Eman Lesmana
    • Sudradjat Supian
    2018-09-01
    https://doi.org/10.14419/ijet.v7i3.20.20574
  • Life insurance, claim risk, collective risk, Value-at-Risk, Collective Modified Value-at-Risk, non-normal distribution.

  • Abstract

    Claim risk is a payment made by the insurance company to the policyholder. Actuaries in insurance companies should be able to measure and control the risk of claims, in order to avoid losses to insurance companies. In this paper we analyze the Geometric-Gamma Collective Modified Value-at-Risk model in life insurance risk. In this research, there is a development of claim risk measure called Collective Modified Value-at-Risk, which is an extension of Collective Risk model. This Collective Modified Value-at-Risk model requires estimation of the mean, variance, skewness, and kurtosis parameters. The result of this research, is that the extent of this model can be applied to the risk of claims amount of non-normal distributed. Thus, the Collective Modified Value-at-Risk model can serve as one of the statistical alternatives for measuring the risk of claims on life insurance.

     

     

  • References

    1. [1] Bortoluzzo, A.B., D. P. Claro, M. A. L. Caetano, R. Artes, 2011, Estimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution, BAR, Curitiba, v. 8, n. 1, art. 3, pp. 37-47, Jan./Mar. 2011, Available online at, http://www.anpad.org.br/bar.

      [2] Dickson, D.C.M. 2005. Insurance Risk and Ruin. Cambridge : Cambridge University Press.

      [3] Diers, D., M.A. Eling, and M.A. Linde, 2012, Modeling Parameter Risk in Premium Risk in Multi-Year Internal Models, Working Papers on Risk Management and Insurance NO. 119, November 2012, pp. 1-25.

      [4] Dionne, G. 2013, Risk Management: History, Difinition and Critique, Cirrelt-2013-17, March 2013, pp. 1-22. www.cirrelt.ca.

      [5] Djuric, Z., 2013, Collective Risk Model in Non-Life Insurance, Economic Horizons, May - August 2013, Volume 15, Number 2, pp. 167 – 175, UDC: 33 eISSN 2217-9232 , UDC: 005.334:368.025.6 ; 347.426.6, doi: 10.5937/ekonhor1302163D.

      [6] Dowd, K. 2002. An Introduction to Market Risk Measurement, John Wiley & Sons, Inc., New Delhi, India.

      [7] Guarda, P., A. Rouabah, and J. Theal, 2012, An MVaR Framework to Capture Extreme Events in Macro-Prudential Stress Tests, Working Paper Series, NO 1464 / AUGUST 2012, pp. 1-46.

      [8] Klugman, S.A., H.H. Panjer, and G.E. Willmot, 1998, Loss Models: From Data to Decision, Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., New York.

      [9] Kolkovska, E.T., 2011, Risk Measures for Classical and Perturbed Risk Processes – A Survey, Pliska Stud. Math. Bulgar. 20 (2011), pp. 121–134.

      [10] Kutub, U.M., I.M. Rafiqul, and R. Taslima, 2011, Mathematical Modeling of Life Insurance Policies, European Journal of Business and Management, ISSN 2222-1905 (Paper) ISSN 2222-2839 (Online), Vol 3, No.4, 2011, pp. 308-321. www.iiste.org.

      [11] Nino, S. and C.G. Paolo, 2010, A Collective Risk Model for Claims Reserve Distribution, 29 th International Congress of Actuaries - ICA 2010, Cape Town – March 7-12th 2010, pp. 1-22.

      [12] Polanski, A., E. Stoja, and R. Zhang, 2013, Multidimensional Risk and Risk Dependence, Paper, pp. 1-38, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK. Email: A.Polanski@uea.ac.uk.

      [13] Sukono, Suyudi, M., Islamiyati, F., and Supian, S. 2017. Estimation Model of Life Insurance Claims Risk for Cancer Patients by Using Bayesian Method. IOP Conf. Series: Materials Science and Engineering 166 (2017) 012022 doi:10.1088/1757-899X/166/1/012022. pp. 1-9.

      [14] Valecký, J., 2016, Modelling Claim Frequency in Vehicle Insurance, ACTA Universitatis Agriculturae Et Silviculturae Mendelianae Brunensis, Volume 64, Number 2, 2016, pp. 683-689. http://dx.doi.org/10.11118/ actaun201664020683.

      [15] Yildirim, I., 2015, Financial Risk Measurement for Turkish Insurance Companies Using VaR Models, Journal of Financial Risk Management, 2015, 4, pp. 158-167, Published Online September 2015 in SciRes. http://www.scirp.org/journal/jfrm. http://dx.doi.org/10.4236/jfrm.2015.43013.

      [16] Zuanetti, D.A., C.A.R. Diniz, and J.G. Leite, 2006, A Lognormal Model for Insurance Claims Data, REVSTAT – Statistical Journal, Volume 4, Number 2, June 2006, pp. 131–142.

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  • How to Cite

    Iqbal Al-Banna Ismail, M., ., S., Talib BIN Bon, A., Hidayat, Y., Lesmana, E., & Supian, S. (2018). Geometric-Gamma Collective Modified Value-at-Risk Model in Life Insurance Risk. International Journal of Engineering & Technology, 7(3.20), 372-376. https://doi.org/10.14419/ijet.v7i3.20.20574

    Received date: 2018-09-29

    Accepted date: 2018-09-29

    Published date: 2018-09-01