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The rolling bond $R(t)$ as defined in your question is a valid numéraire. Indeed, this bond can synthetized with the following iterative trading strategy in basic assets: At any time $T_i\in\{T_0,\dots,T_{m(t)-1}\}$, invest your available wealth into the spot-starting zero-coupon bond expiring at $T_{i+1}$, with price $P(T_i,T_{i+1})$. At $T_{i+1}$, you ...


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