European Actuarial Journal

, Volume 8, Issue 2, pp 461–485 | Cite as

Optimal management of immunized portfolios

  • Riccardo CesariEmail author
  • Vieri Mosco
Original Research Paper


We generalize the contribution of Fong and Vasicek (Financ Anal J 39:73–78, 1983a; Innov Bond Portf Manag Durat Analy Immun 1983:227–238, 1983b; J Financ 39:1541–1546, 1984) by developing a risk-return optimization problem for immunized life insurance portfolios. The M2 measure of risk for arbitrary changes of the term structure of interest rates is used for a bond portfolio with duration matched to a given liability horizon. The immunization case becomes a “passive” strategy among an entire menu of active management decisions in which a partial risk minimization is exchanged for more return potential. As in the classical Markowitz (Portfolio Selection, New York, Wiley, 1959) approach, an efficient frontier at the given horizon provides the optimal tradeoff between risk and return. An empirical application to insurance companies shows that such a perspective may be proved useful to highlight which segregated funds can be re-positioned over the efficient frontier, at the chosen level of the firm’s risk appetite.


Insurance companies Immunization Convexity Fong–Vasicek theorem Efficient frontier 

JEL Classification

G22 G11 G12 



We thank Antonio De Pascalis, Lino Matarazzo, Enzo Orsingher, Stefano Pasqualini, Fabio Polimanti, Giovanni Rago, Arturo Valerio and the participants to a seminar of IVASS and Bank of Italy for their comments. A special thank to Oldrich Vasicek and two anonymous referees for their detailed comments and suggestions to a previous version of the paper. All remaining errors are ours.


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Copyright information

© EAJ Association 2018

Authors and Affiliations

  1. 1.University of BolognaBolognaItaly
  2. 2.IVASSRomeItaly
  3. 3.IVASS, Research DepartmentRomeItaly

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