  This paper is a synthesis of the theories of portfolio generating functions
and rational option pricing. For a family of n >= 2 assets with prices
represented by strictly positive continuous semimartingales, a contingent claim
function is a scalable positive C^{2,1} function of the asset prices and time.
We extend the theory of portfolio generation to measure the value of portfolios
generated by contingent claim functions directly, with no numeraire portfolio.
We show that if a contingent claim function satisfies a particular parabolic
differential equation, then the value of the portfolio generated by that
contingent claim function will replicate the value of the function. This
differential equation is a general form of the Black-Scholes equation.
