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Immunization and Max–Min Optimal Control

Author

Listed:
  • L. L. Ghezzi

    (Carlo Cattaneo University
    Politecnico di Milano)

Abstract

A model of a term structure of interest rates is conceived in which disturbances are unknown and bounded. Arbitrage opportunities are ruled out by imposing suitable constraints to the disturbances. This sets the stage for casting a well-known immunization problem as a max-min optimal control problem. Dynamic programming is then used to obtain the analytical solution to such a problem. In this manner, a well-known immunization policy is proved to be optimal in a dynamic setting.

Suggested Citation

  • L. L. Ghezzi, 1997. "Immunization and Max–Min Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 701-711, December.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:3:d:10.1023_a:1022686225209
    DOI: 10.1023/A:1022686225209
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    References listed on IDEAS

    as
    1. Khang, Chulsoon, 1983. "A Dynamic Global Portfolio Immunization Strategy in the World of Multiple Interest Rate Changes: A Dynamic Immunization and Minimax Theorem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(3), pages 355-363, September.
    2. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    3. Fong, H Gifford & Vasicek, Oldrich A, 1984. "A Risk Minimizing Strategy for Portfolio Immunization," Journal of Finance, American Finance Association, vol. 39(5), pages 1541-1546, December.
    4. Montrucchio, Luigi & Peccati, Lorenzo, 1991. "A note on Shiu--Fisher--Weil immunization theorem," Insurance: Mathematics and Economics, Elsevier, vol. 10(2), pages 125-131, July.
    5. Fisher, Lawrence & Weil, Roman L, 1971. "Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies," The Journal of Business, University of Chicago Press, vol. 44(4), pages 408-431, October.
    6. Bierwag, G. O., 1979. "Dynamic portfolio immunization policies," Journal of Banking & Finance, Elsevier, vol. 3(1), pages 23-41, April.
    7. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    8. Bierwag, G O & Khang, Chulsoon, 1979. "An Immunization Strategy Is a Minimax Strategy," Journal of Finance, American Finance Association, vol. 34(2), pages 389-399, May.
    9. Ritchken, Peter & Boenawan, Kiekie, 1990. "On Arbitrage-Free Pricing of Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 45(1), pages 259-264, March.
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