Risk-neutral price ($V_t=B_t{\mathbb{E}}_Q[H/B_T\mid {\mathcal{F}}_t]$)

In an arbitrage-free finite market, a risk-neutral price expresses a replicable terminal financial payoff $H$ as a discounted expectation under an equivalent martingale measure $Q$. For a positive bank account $B$, its time-$t$ price isThis is a statement about claim replication and no-arbitrage, rather than the physical probability of future outcomes. For a one-period binomial market with multipliers $d<R<u$, the risk-neutral up probability is $q=(R-d)/(u-d)$ and $V_0=(q{H}_u+(1-q)H_d)/R$. A nonreplicable payoff in an incomplete market can give different values under different martingale measures; uniqueness then needs additional assumptions.