The Impact of Large Claims on Actuarial Decisions


In this chapter, we elaborate on and develop some ideas which were already presented in Section 1.1. Recall that the expectation of the total claim amount determines the net premium. Based on the net premium, the insurer determines the total premium that must be paid by the policy holder. We start in Section 17.1 with the calculation of the df, expectation and variance of the total claim amount.


Generalize Pareto Distribution Risk Process Claim Size Large Claim Generalize Pareto 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 2.
    For details and further references, see, e.g., Kremer, E. (1992). The total claims amount of largest claims reinsurance revisited. Blätter DGVM 22, 431–439.Google Scholar
  2. 3.
    Also see Kuon, S., Radtke, M. and Reich, A. (1993). An appropriate way to switch from the individual risk model to the collective one. Astin Bulletin 23, 23–54.CrossRefGoogle Scholar
  3. 4.
    For an elementary introduction to premium principles see Straub, E. (1989). Non-Life Insurance Mathematics. Springer, Berlin.Google Scholar
  4. 5.
    Schnieper, R. (1993). Praktische Erfahrungen mit Grossschadenverteilungen. Mitteil. Schweiz. Verein. Versicherungsmath., 149–165.Google Scholar
  5. 6.
    McNeil, A.J. (1997). Estimating the tails of loss severity distributions using extreme value theory. ASTIN Bulletin 27, 117–137.CrossRefGoogle Scholar
  6. 7.
    Gerathewohl, K. (1976). Rückversicherung: Grundlagen und Praxis. Verlag Versicherungswirtschaft.Google Scholar
  7. 8.
    See, e.g., Vylder, de F. (1997). Advanced Risk Theory. Editrans de l’Université Bruxelles.Google Scholar
  8. 9.
    Also see Vylder, de F. and Goovaerts, M.J. (1988). Recursive calculation of finite-time ruin probabilities. Insurance: Mathematics and Economics 7, 1–7.MATHCrossRefGoogle Scholar
  9. 10.
    Presented at the 35th ASTIN meeting (Cologne, 1996) of the DAV.Google Scholar
  10. 11.
    Supplementary details can be found in Reiss, R.-D., Radtke, M. and Thomas, M. (1997). The T-year initial reserve. Technical Report, Center for Stochastic Processes, Chapel Hill.Google Scholar
  11. 12.
    Embrechts, P. and Klüppelberg, C. (1993). Some aspects of insurance mathematics. Theory Probab. Appl. 38, 262–295.CrossRefGoogle Scholar
  12. 13.
    See, e.g., Hipp, C. and Michel, R. (1990). Risikotheorie: Stochastische Modelle und Statistische Methoden. Verlag Versicherungswirtschaft, Karlsruhe.MATHGoogle Scholar
  13. 14.
    Bahr von, B. (1975). Asymptotic ruin probabilities when exponential moments do not exist. Scand. Actuarial J., 6–10. In greater generality dealt with in Embrechts, P. and Veraverbeke, N. (1982). Estimates for the probability of ruin with special emphasis on the probability of large claims. Insurance: Mathematics and Economics 1, 55–72.Google Scholar

Copyright information

© Birkhäuser Verlag AG 2007

Personalised recommendations