= Path-dependent contingent claim
{title2=$C=F((S_u)_{0\le u\le T})$}
= Path-dependent claim
{synonym}
A <contingent claim> whose payoff depends on the underlying price history, rather than only its terminal price. <Asian options> use averages, <barrier options> use whether a threshold has been crossed, and <lookback options> use running extrema. In the <Black-Scholes model>, the Brownian <Martingale representation theorem> still gives a <replicating strategy>; its <portfolio wealth> need not be a function of the current stock price alone. Adding a running integral or extremum can give a finite-dimensional state for pricing.
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