= Multi-period dividend pricing identity
{title2=$B_rV_r=\mathbb E_Q[B_nV_n+\sum_{j=r+1}^nB_jD_j\mid\mathcal F_r]$}
For an <integrable> discrete trading strategy under an <equivalent martingale measure>, discounted <portfolio wealth> plus accumulated discounted strategy payments is a <martingale>. Conditioning its terminal value gives the displayed identity. A formula involving future payments alone requires terminal liquidation, $V_n=0$, or inclusion of that terminal value in the final payment. For an <attainable claim> paid only at maturity, liquidation yields its usual conditional discounted <expected value>.
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