Portfolios Generated by Contingent Claim Functions, with Applications to Option Pricing

Abstract

In a market of stocks represented by strictly positive continuous semimartingales, a contingent claim function is a positive C^{2, 1} function of the stock prices and time with a given terminal value. If a contingent claim function satisfies a certain parabolic differential equation, it will generate a portfolio with value process that replicates the contingent claim function. This parabolic differential equation is a general form of the Black-Scholes equation.