Advertisement

Blätter der DGVFM

, Volume 14, Issue 4, pp 579–584 | Cite as

Some Mathematical Aspects of Claim Number Processes with the Markov Property

  • J. Haezendonck
Article

Summary

We show with a counterexample that the amount of the jumps of a claim number process may be different from one even if the usual condition on the right hand derivatives of the transition probabilities is fulfilled. We strengthen this condition in order to ensure the existenc of only jumps of amount one and we prove that the claim number process verifies a general Markov property provided some weak regularity assumptions on the transition probabilities are satisfied.

Keywords

Usual Condition Markov Property Dominate Convergence Theorem Mathematical Aspect Sample Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bauer, H.: Probability Theory and Elements of Measure Theory. Holt, Rinehart and Winston, Inc. (1972).MATHGoogle Scholar
  2. [2]
    Bühmann, H: Mathematical Methods in Risk Theory. Springer Verlag (1970).Google Scholar
  3. [3]
    Courrège, P. andPriouret, P.:Temps d’arrÊt d’une fonction aléatoire: Relations d’équivalence associées et propriétés de décomposition. Publ. Inst. Statist. Univ. Paris;14 (1965), 245–274.MathSciNetGoogle Scholar
  4. [4]
    Heyer, H.: Ma\theoretische ErgÄnzungen zur Risikotheorie (Struktur des Risikoprozesses). BlÄtter der DGVM;10 (1972), 451–466.MATHCrossRefGoogle Scholar

Copyright information

© DAV/DGVFM 1980

Authors and Affiliations

  • J. Haezendonck
    • 1
  1. 1.Antwerpen

Personalised recommendations