Chapter 4. Distributions of Aggregate Claim Amount

  1. Tomasz Rolski1,
  2. Hanspeter Schmidli2,
  3. Volker Schmidt3 and
  4. Jozef Teugels4

Published Online: 27 MAY 2008

DOI: 10.1002/9780470317044.ch4

Stochastic Processes for Insurance & Finance

Stochastic Processes for Insurance & Finance

How to Cite

Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999) Distributions of Aggregate Claim Amount, in Stochastic Processes for Insurance & Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470317044.ch4

Author Information

  1. 1

    Mathematical Institute, University of Wrocław

  2. 2

    Department of Theoretical Statistics, Aarhus University, Denmark

  3. 3

    Faculty of Mathematics and Economics, University of Ulm, Germany

  4. 4

    Department of Mathematics, Catholic University of Leuven, Belgium

Publication History

  1. Published Online: 27 MAY 2008
  2. Published Print: 17 FEB 1999

ISBN Information

Print ISBN: 9780471959250

Online ISBN: 9780470317044

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Keywords:

  • aggregate claim;
  • insurance mathematics;
  • individual model;
  • collective model;
  • Poisson compounds

Summary

The prelims comprise:

  • Individual and Collective Model

  • Compound Distributions

  • Claim Number Distributions

  • Recursive Computation Methods

  • Lundberg Bounds

  • Approximation by Compound Distributions

  • Inverting the Fourier Transform