A Proposition on the Martingale Representation Theorem and on the Approximate Hedging of Financial Contingent Claims

Abstract

In this short communication paper, we revisit the problem of the hedging of financial contingent claims using the mean-square criterion. We prove that in incomplete market, some probability measure Q~P can be identified so that {S_n} becomes {F_n}-martingale under Q. This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure Q.