 Arrow–Debreu state price

On a finite state space, the Arrow–Debreu state price is the current price of a payoff equal to one in state $s$ and zero elsewhere. It equals the physical state probability times the state-price density in that state. With a riskless asset of deterministic prices $B_0,B_1$, the Arrow state prices sum to $B_0/B_1$. Normalizing them gives the risk-neutral probabilities, while division by the physical probabilities instead recovers the pricing density.