= Binomial-market probability density
{title2=$L_n=(q/p)^{N_n}((1-q)/(1-p))^{n-N_n}$}
With independent up moves of physical probability $p$ and risk-neutral probability $q$, the <Radon-Nikodym derivative> on the first $n$ periods is the displayed likelihood ratio, where $N_n$ counts up moves. Its conditional one-step multiplier has physical expectation one, so $L_k$ is a positive mean-one <martingale>. The terminal <state-price density> is $L_n/B_n$ for deterministic bank-account value $B_n$.
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