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On The Impact Of Hidden Trends For A Compound Poisson Model With Pareto-Type Claims

Author

Listed:
  • PETER GRANDITS

    (Financial and Actuarial Mathematics, Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8-10/105-1, A-1040 Vienna, Austria)

  • REINHOLD KAINHOFER

    (Financial and Actuarial Mathematics, Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8-10/105-1, A-1040 Vienna, Austria)

  • GRIGORY TEMNOV

    (Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, University College Cork, Ireland)

Abstract

We consider a compound-Poisson model with Pareto-type claims. In contrast to the classical case, where the claims are assumed to be iid., we assume that scaling and location parameters of the Pareto distribution follow a certain trend. We investigate the impact of this trend on parameter estimation and on the VaR (Value-at-Risk), if one mis-specifies (or even neglects) this trend. In the first part we show a consistency result for the mis-specified model, in the second part the deviations of the true parameters from the ones obtained by applying an iid. procedure is measured. Finally we study the impact of the mis-specification on a typical risk measure like the VaR.

Suggested Citation

  • Peter Grandits & Reinhold Kainhofer & Grigory Temnov, 2010. "On The Impact Of Hidden Trends For A Compound Poisson Model With Pareto-Type Claims," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 959-978.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:06:n:s0219024910006066
    DOI: 10.1142/S0219024910006066
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