Risk Theory in Insurance

  • Tomas Cipra


Chapter 22 presents basic formulas of risk theory in the context of insurance: 22.1. Collective Risk Model, 22.2. Aggregate Claim Distribution, 22.3. Copula, 22.4. Credibility Premium, 22.5. Ruin Probability, 22.6. Deductible, 22.7. Calculations for Bonus-Malus Systems.


Risk Class Moment Generate Function Risk Parameter Archimedean Copula Claim Amount 
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Further Reading

  1. Booth, P., Chadburn, R., Cooper, D., Haberman, S., James, D.: Modern Actuarial Theory and Practice. Chapman and Hall/CRC, London (1999)MATHGoogle Scholar
  2. Daykin, C.D., Pentikäinen, T., Pesonen, M.: Practical Risk Theory for Actuaries. Chapman and Hall, London (1994)MATHGoogle Scholar
  3. Denuit, M., Dhaene, J., Goovaerts, M., Kaas, R.: Actuarial Theory for Dependent Risks: Measures, Orders and Models. Wiley, New York (2005)CrossRefGoogle Scholar
  4. Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling External Events for Insurance and Finance. Springer, Berlin (1997)CrossRefGoogle Scholar
  5. Heilmann, W.-R.: Fundamentals of Risk Theory. VVW, Karlsruhe (1988)MATHGoogle Scholar
  6. Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern Actuarial Risk Theory, Using R. Springer, Berlin (2008)MATHCrossRefGoogle Scholar
  7. Klugman, S.A., Panjer, H.H., Willmot, G.E.: Loss Models. Wiley, New York (1998)MATHGoogle Scholar
  8. Mack, T.: Schadenversicherungsmathematik. VVW, Karlsruhe (2002)Google Scholar
  9. Nelsen, R.B.: An Introduction to Copulas. Springer, New York (1999)MATHCrossRefGoogle Scholar
  10. Straub, E.: Non-Life Insurance Mathematics. Springer, Berlin (1988)MATHCrossRefGoogle Scholar
  11. Teugels, J., Sundt, B. (eds.): Encyclopedia of Actuarial Science. Wiley, New York (2004)MATHGoogle Scholar
  12. Wolfsdorf, K.: Versicherungsmathematik (Teil 2: Theoretische Grundlagen, Risikotheorie, Sachversicherung). Teubner, Stuttgart (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dept. of Statistics, Faculty of Mathematics and PhysicsCharles University of PraguePragueCzech Republic

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