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2 results

  • On Immunisation and S-Convex Extremal Distributions

  • C. Courtois, M. Denuit
  • Journal:
    Annals of Actuarial Science / Volume 2 / Issue 1 / March 2007
    Published online by Cambridge University Press:
    10 May 2011, pp. 67-90

  • The paper concerns the interest risk management of insurance companies or banks. Classes of stochastic order relations for arbitrary discrete random variables are used to find extremal strategies of immunisation in the context of deterministic immunisation theory. In a special case, the results obtained by Hürlimann (2002) are extended to conditions for immunisation under arbitrary S-convex or S-concave shift factors of the term structure of interest rates. The notion of the Shiu measure is generalised to an immunisation risk measure, accounting for more moments of the asset and liability risks.

  • Local Moment Matching and S-convex Extrema

  • Cindy Courtois, Michel Denuit
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 37 / Issue 2 / November 2007
    Published online by Cambridge University Press:
    17 April 2015, pp. 387-404
    Print publication:
    November 2007
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  • The paper is devoted to the local moment matching method and its links with the discrete version of the s-convex extremal distributions. It is well-known that the local moment matching method can produce some negative masses. Connecting the local moment matching method to the discrete s-convex extrema gives an explicit criterion that explains why (and says when) the local moment matching method gives some negative mass.