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On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

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  • Rastislav Potocký
  • Helmut Waldl
  • Milan Stehlík

Abstract

The problem that assets of a fund are not sufficient to cover its liabilities is of extreme importance both for its members as well as for fund managers. We show that this problem can be solved via total claims distributions and give answers to the following questions: How much money will be needed in the first pillar in order to satisfy the requirements of pensioners in a time horizon and which groups of working people should join also the second pillar because their benefits from it will be greater than those from the first pillar? Though the paper concentrates primarily on the situation with Slovakian pension funds we believe that our findings are more general. We show that the alternative methods should be used for calculation of extremes. We discuss the so-called barrier strategy for treating the surplus of an insurance company and bring some new results concerning it.

Suggested Citation

  • Rastislav Potocký & Helmut Waldl & Milan Stehlík, 2014. "On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products," Prague Economic Papers, Prague University of Economics and Business, vol. 2014(3), pages 349-370.
    • Handle: RePEc:prg:jnlpep:v:2014:y:2014:i:3:id:488:p:349-370
    DOI: 10.18267/j.pep.488
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    References listed on IDEAS

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    1. Michal Uherek & Milan Stehlík & Luboš Střelec, 2011. "On robust analysis of paycheck: case study," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 59(4), pages 371-378.
    2. Ulrich Hommel & Mischa Ritter, 2005. "New Approaches to Managing Catastrophic Insurance Risk," Springer Books, in: Michael Frenkel & Markus Rudolf & Ulrich Hommel (ed.), Risk Management, edition 0, pages 341-367, Springer.
    3. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
    4. Edward Whitehouse, 2009. "Pensions During the Crisis: Impact on Retirement Income Systems and Policy Responses," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 34(4), pages 536-547, October.
    5. Brazauskas, Vytaras & Serfling, Robert, 2003. "Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 365-381, November.
    6. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. David J. Hand, 2018. "Statistical challenges of administrative and transaction data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(3), pages 555-605, June.

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    More about this item

    Keywords

    light- and heavy-tailed distributions; catastrophic events; claims; first and second; robust approach; Johnson estimators; the 20-80 rule;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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