Under parallel shifts, a bond portfolio Q that has the same present value and the same (modified) duration as the liability, PV[Q] = PV[L], and Dm [Q] = Dm [L] implies PV[Q] = PV[L] , (2)
where PV denotes present values after a parallel shift. This indicates that duration is a key measure of any sequential immunisation strategy. We require that Dm [Q](t) = Dm [L](t) at all dates t = 0, 1, 2, . . . , H, (3.t)
in addition to the present-value condition (1.t). 1.4 Self-financing Strategies If at date…
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