Maxmin portfolios in financial immunization

The existence of maxmim bond portfolios is proved in very general contexts, and so for instance, this existence holds if an immunized portfolio does not exist but all the considered portfolios have duration equal to the investor planning period. To characterize the maxmin portfolio, saddle point conditions are found, and from them, an algorithm is given. This algorithm permits to find the maxmin portfolio in practical situations. Relations between maxmin portfolios and the ones minimizing the dispersion measures (for instance, the M-squared or the Ñ measure) are also studied. In particular, it will be proved that minimizing the dispersion measure and looking for maxmin portfolio are equivalent strategies only when we are working with pure discount bonds. Finally, as a consequence of the obtained results, two new strategies to invest are proposed.