= State-price budget constraint
{title2=$\mathbb E[\zeta_T X]+\mathbb E\int_0^T\zeta_t c_t\,dt\leq w$}
A <state-price density> converts terminal wealth and consumption into initial cost. For a nonnegative admissible <self-financing portfolio> with consumption, the deflated wealth plus cumulative deflated consumption is a <supermartingale>, giving $\mathbb E[\zeta_TX]+\mathbb E\int_0^T\zeta_tc_tdt\leq w$. In a <complete market>, an integrable nonnegative terminal claim with full budget equality is replicable.
Back to article page
