Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-26T16:42:20.070Z Has data issue: false hasContentIssue false
  • English
  • Français

On Immunisation and S-Convex Extremal Distributions

Published online by Cambridge University Press:  10 May 2011

C. Courtois  and
M. Denuit
C. Courtois
Affiliation:
Commission Bancaire, Financière et des Assurances, Rue du Congrès 12/14, B-1000 Bruxelles, Belgium., Email: Cindy.Courtois@cbfa.be
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

ImmunisationExtremal StrategiesS-Convex OrderInterest Rate Risk
Type
Papers
Information
Annals of Actuarial Science , Volume 2 , Issue 1 , March 2007 , pp. 67 - 90
Copyright
Copyright © Institute and Faculty of Actuaries 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Courtois, C. & Denuit, M. (2006). S-convex extremal distributions with arbitrary discrete support. Working paper WP06–10, Institut des Sciences Actuarielles, UCL.Google Scholar
Denuit, M., Lefèvre, CL. & Shared, M. (1998). The s-convex orders among real random variables, with applications. Mathematical Inequalities & Applications, 1, 585–613.CrossRefGoogle Scholar
Denuit, M., Lefèvre, CL. & Utev, S. (1999). Stochastic orderings of (convex/concave)-type on an arbitrary grid. Mathematics of Operations Research, 24, 835–846.CrossRefGoogle Scholar
Fong, H.G. & Vasicek, O.A. (1984). A risk minimising strategy for portfolio immunization. The Journal of Finance, 39, 1541–1546.Google Scholar
Haynes, A.T. & Kirton, R.J. (1952). The financial structure of a life office. Transactions of the Faculty of Actuaries, 21, 141–197, discussion 198–218.CrossRefGoogle Scholar
Hürlimann, W. (2002a). On immunization, stop-loss order and the maximum Shiu measure. Insurance: Mathematics and Economics, 31, 315–325.Google Scholar
Hürlimann, W. (2002b). On immunization, s-convex orders and the maximum skewness increase. (available at www.mathpreprints.com)Google Scholar
Hürlimann, W. (2003). The algebra of cash flows: theory and application. In: Jain, L.C. & Shapiro, A.F. (eds.). Intelligent and other computational techniques in insurance — theory and applications (series on innovative intelligence), Chapter 18. World Scientific Publishing Company.Google Scholar
Karlin, S. & Studden, W.J. (1966). Tchebycheff systems with applications in analysis and statistics. Wiley Interscience, New York.Google Scholar
Moll, D.P. (1909). On the effect of a rise, or fall, in market values of securities, on the financial position and reserves of a life office. Journal of the Institute of Actuaries, 43, 105–107.Google Scholar
Montrucchio, L. & Peccati, L. (1991). A note on Shiu-Fisher-Weil immunization theorem. Insurance: Mathematics and Economics, 10, 121–131.Google Scholar
Nawalkha, S.K., Soto, G.M. & Beliaeva, N. (2005). Interest rate risk modeling: the fixed income valuation course. Wiley.Google Scholar
Panjer, H.H. (1998). Financial economics: with applications to investments, insurance and pensions. The Society of Actuaries, Schaumburg, IL.Google Scholar
Poitras, G. (2007). Federick R. Macaulay, Frank M. Redington and the emergence of modern fixed income analysis. Chapter 4 in Pioneers of financial economics (vol. 2), Poitras, Geoffrey (ed.), Cheltenham U.K.: Edward Elgar.Google Scholar
Redington, F.M. (1952). Review of the principles of life-office valuations. Journal of the Institute of Actuaries, 78, 286–340 (with discussion).CrossRefGoogle Scholar
Shiu, E.S.W. (1986). A generalization of Redington's theory of immunization. Actuarial Research Clearing House 1986, 2, 61–81.Google Scholar
Shiu, E.S.W. (1988). Immunization of multiple liabilities. Insurance: Mathematics and Economics, 7, 219–224.Google Scholar
Shiu, E.S.W. (1990). On Redington's theory of immunization. Insurance: Mathematics and Economics, 9, 171–175.Google Scholar
Uberti, M. (1997). A note on Shiu's immunization results. Insurance: Mathematics and Economics, 21, 195–200.Google Scholar
Wallas, G.E. (1960). Immunization. Journal of the Institute of Actuaries Students' Society, 15, 345–357.Google Scholar