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

Abstract

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.